As we mentioned, through the Shapley-Curtis debate, around the 1930's astronomers were gradually coming around to the conclusion that some of the nebulae were objects external to the Milky Way and essentially similar to the it. This was not an new concept, the idea of ``Island Universes'' had already been proposed by many before, including Immanuel Kant. However there had not been any substantial evidence to support these essentially philosophical positions. Arabs had known of the existence of the nebulousities like the Magellanic clouds and Andromeda that are now known to be external galaxies. Spectroscopic studies towards the end of the last century led to the recognition of two groups of nebulae. One group had emission lines and were therefore gaseous and other had continuous spectrum and thus must be comprised of many stars. But it wasn't until 1920's, after the large telescopes of Mount Wilson Observatory identified individual stars in the Andromeda Galaxy, that the similarity of these nebulae and the Milky Way was established. Edwin Hubble, one of the most important observers in astronomy, recognized some of the stars in the Andromeda nebula to be Cepheids. Using their characteristic period-luminosity relationship he could find out the distance to the nebula. He found it was at a distance far outside the Milky Way. He found cepheids in other galaxies as well and could measure the distance to them. It had already been known since the time of Slipher that galaxies are receding away from us. Hubble plotted the distance of the galaxies against the speed of their recession and found that the distant galaxies were receding faster. This discovery had enormous impact on our understanding of the Universe. For the moment though we will concentrate on another contribution due to Hubble. Which is the classification of different types of galaxies.
The classification system introduced by Hubble is still being used by astronomers today. He divided the galaxies according to how they appeared, i.e., morphologically, into three basic types; Ellipticals, normal & barred Spirals and Irregulars.
Elliptical galaxies appear smooth and as their name suggests,
elliptical in the sky. If their semi-major axis is a and the semi
minor axis is b, then the extra label they get is 10 times their
ellipticity, where ellipticity is defined is, 
. So a round elliptical galaxy is a E0 galaxy. An E1 galaxy is
flatter, and so on. Galaxies appear to be no flatter than E7.
Lenticular galaxies are smooth like elliptical galaxies, but they have small disks in them which differentiates them from elliptical galaxies. They are designated as S0 galaxies.
Spirals have their stars distributed in a flat disk. As their name suggests they are characterized by the presence of spiral arms in these disks. They are not smooth like the ellipticals, but have dark patches in them. The most prominent part of the spirals is the disk of stars with the spiral arms. But in the center of the disks they have spherical bulge. Around the disk they have distributed a small number of stars in a sphere that is called the galaxy's spheroidal halo. The spiral galaxies are divided into three groups, Sa, Sb and Sc. Sa's are galaxies with a prominent bulge and tightly wound arms. Sb's have a less arms/bulge contrast and more open arms and finally Sc's have the much fainter bulges compared to their arms that are very loosely bound. Aside from the ``normal'' spirals there are also the barred spirals whose central bulge are elongated like a bar instead of being spherical. Barred spirals are also separated into three subclasses, SBa, SBb and SBc characterized by arm to bulge contrast and windedness of arms. Some spiral galaxies fall in intermediate classes as well, like Sab, SBbc, etc.
Irregular galaxies, as may be expected, are those that don't fit into either category of elliptical and spiral galaxies. They are very irregular and have lots of dark patches in them.
Aside from these morphological distinctions that define the three
classes, there are other features that vary along this sequence of
galaxies. The stellar populations are different along the
sequence. Ellipticals have primarily population II stars. These are
red, old stars, mostly G, K and M giants. Spirals on the other hand
have a mixture of population I and population II stars. The red old
giant stars tend to be around the spheroidal and inter-arm disk region
of spirals. Hot blue young stars on the other hand are usually in the
spiral arms. The light in Spirals are dominated by young A
stars. Spirals have a lot of gas, nearly 
of the mass in visible
matter is gas. Elliptical galaxies also have some gas though not in as
large quantities. The gas in Ellipticals is mostly hot gas that is
visible through its radiation of intense X-ray. Spirals on the other
hand have cold gas that appear as dark patches in the galaxy. They are
the birth places of stars. Irregulars have large amounts of cold gas in
them. They also have active star formation going on in them.
Spirals are the usually similar in size to the Milky Way or Andromeda
with about 
stars in each galaxy. Ellipticals come in two
varieties, giants which have upto 
stars and dwarfs which
have only 
stars. Irregulars tend to be small galaxies like the
Magellanic clouds.
Elliptical and spiral galaxies occupy different regions of the Universe. Ellipticals tend to crowd in regions with higher density of galaxies. Spirals on the other hand dominate the regions with fewer galaxies.
There are two competing models for the formations of different types of galaxies. Both these models are still at very preliminary stages and considerable work needs to be done before any firm conclusion can be drawn on which is appropriate for the galaxies we observe. Conceivably reality is considerably more complex and some mixture of either model or perhaps even a third model is more appropriate.
In this model the fate of a galaxy is decided by where it is born. Galaxies are born when gas and dark matter collapse under the effect of gravity and stars are born in this collapsing matter. This collapse starts early if there are many such clumps around that can collapse and late if the clump is in a relatively empty part of the Universe. If the collapse starts early in the life of the Universe it will proceed fast. The stars form early in the collapse. All the gas is quickly exhausted into forming stars before the collapsing gas has a chance to settle into a disk and then form stars. So the stars start off in a spherical configuration moving in all directions. If stars don't start off in a disk they cannot settle to a disk so we end up with a galaxy that has little cold gas with stars in a nearly spherical distribution moving in all directions. Because it is old (collapse having started early) the stars will also be old and red. And we end up with an elliptical galaxy.
The gas cloud that is starting to collapse in an emptier part of space on the other hand starts later and collapses more slowly. The gas isn't exhausted into making stars and lots of it can settle into a flat disk (which is what gas wants to do as its collapsing). A few stars are born in a spherical distribution moving in all directions, which form the spheroidal halo of a spiral galaxy. Most of the stars form in the disk and stay in the disk resulting in a spiral galaxy. Also because there is gas left over from the star formation there can be young stars. The segregation of elliptical and spiral galaxies according to the local density of galaxies is explained because of the location of their birth. This model may have a problem explaining the large number of dwarf ellipticals in a small group like our local group in a region of the Universe with low density of galaxies.
Although galaxies look stationary and immutable they are infact constantly subject to violent interactions. They can have close passes and actual collisions, quite frequently in regions of higher density of galaxies. Just as you are more likely to bump into more people in a crowded street than an empty park. It is an observed fact that a large number of galaxies are interacting, colliding and even merging together. Given this fact the merger model suggests that all galaxies to start off were like spiral galaxies, with stars and gas in disks. Then as they merged and interacted with each other the remnant product was an elliptical galaxy. This is why elliptical galaxies are in excess in regions with high density of galaxies. And also why the giant elliptical galaxies are bigger than the spirals. On the other hand the model may have problems explaining two categories of ellipticals, the giant and the dwarf.
This is still a very active field of astronomy and we will not be able to decide on the correct model until we have more information through better observation of early galaxies and better theoretical predictions on what to expect from each model.
One of the topics that astronomers have invested huge effort into has been the measurement of distances to galaxies. As the brightest building blocks of the Universe they light up the furthest reaches of the Universe. So to measure the distances to the farthest galaxies is to measure the extent of the Universe.
The nearest galaxy to us is the Large Magellanic Cloud (LMC), which is at a distance of 50,000 parsecs. Measuring parallaxes of stars is out of the question at such distances. Edwin Hubble used the cepheid variable stars to measure distances to the LMC. Remember Harlow Shapley had used Henrietta Leavitt's data to calibrate the relationship between the brightness and the period of variation of the stars. So by measuring the time between two peaks of brightness of a cepheid it was possible to tell how bright it was. This meant Hubble could measure the distance to LMC from the cepheids in it. He used this technique on other nearby galaxies, like Andromeda, as well.
In the meantime Slipher had taken spectrographic pictures of galaxies and found that absorption lines in the spectra were redshifted as well as varying across the face of the galaxy. The variation across the face was taken to mean the galaxies rotated, where as the overall redshift of spectra that the galaxies as a whole were receding from us. Hubble plotted these recession velocity against the distances he had measured of galaxies and found that they were related. The further a galaxy was the faster it was receding away from us. If v is the speed of recession of a galaxy at a distance d from us, then, v = Hd, where H is a constant called the Hubble's constant. This can be understood as a situation where every galaxy moves away from every other galaxy in the Universe. Say there is one galaxy at a distance d from us, then of course it moves away from us at a speed v=Hd. Another galaxy at a distance d from this galaxy (i.e., at a distance 2d from us), will move at a speed v=Hd from that galaxy and thus at a speed 2v = 2Hd from us (since it is moving at speed v away from an object moving at a speed v away from us, so the relative speed is the sum of these two speeds). This is a momentous discovery that took us away forever from a static, unchanging Universe to a constantly evolving one. And because of the importance of this discovery people have checked this result many times. As we saw in the case of Trumpler's discovery of dark clouds in the galaxy, there is a need for independent measures of significant quantities. Since Hubble several techniques of measuring distances have been used.
If you have ever looked at pictures by Seurat you must have noticed the borders of the paintings that he used to make himself. Seen from a distance they look like a blue background at the bottom of the painting that gradually changes color to become a red background at the top of the painting. If you go right up close to the painting you can see the blue and red backgrounds are actually made of many small dots of painting. From a distance the eye can't tell such small details and the dots all wash together to form a smooth background. This applies to distant galaxies as well. If a galaxy is far away it will appear smoother than a galaxy that is nearer. By quantifying the amount of grainy-ness in the image of a galaxy we can get an estimate on the distance to the galaxy. This method of measuring distance to a galaxy is called the Surface Brightness Fluctuation method.
Another approach to distance measurement is the method of standard candle. In this method use is made of some relationship between of the brightness of an object and some other attribute, or more commonly of the fact that the intrinsic brightness of all objects of the same kind are the same. One of the brightest standard candles in the Universe are the galaxies. Remember the speed of rotation of a Spiral galaxy is connected with the amount of matter in the galaxy. Unless the fraction of dark matter to visible matter varies arbitrarily from galaxy to galaxy it stands to reason that the galaxy with more dark matter will also have more visible matter. In this case it can be expected that how fast a galaxy rotates is connected to how bright it is. This can be established by measuring the speed of rotation of galaxies whose distances are known. Once the relationship between rotation speed and brightness has been established empirically we can use the relatively easily measured rotation speed to find out the intrinsic brightness of a galaxy and hence its distance. This is called the Tully-Fisher relation. A similar results stands for Elliptical galaxies. In the case of these galaxies however instead of rotation speed (because they don't have ordered rotation), the average random velocities of the stars is related to the intrinsic brightness of the galaxy. This is called the Faber-Jackson relation.
Another approach has been to find alternatives to the use of cepheids to measure distances to the nearest galaxies. One method that has been attempted is to use the supernovae. They are very bright they can be seen out to many other galaxies. Using them as standard candles distances to distant galaxies where they have been seen can be measured.
The point of using all the different methods of measuring distances is that while they each individually may not be sufficiently convincing, that all these different independent methods of measurement yield roughly the same results give us confidence in the scale of the Universe that we measure.
As mentioned before Vesto Slipher had observed the speed of recession
of galaxies. Spectral lines from external galaxies were red-shifted
signifying they were moving away from us, according to the law later
discovered by Hubble. However the spectral lines were also redder on
one side of the galaxy than on the other. That indicated that one side
of the galaxy was moving away from us faster than the other side. This
was taken to mean the galaxy was rotating. So one side was moving
towards us and other side moving away from us, over and above the
recession velocity the galaxy had as a whole. It is possible to
measure the mass of the galaxy from the speeds of rotation from
Newton's gravity, much the same way the Sun's mass can be estimated
from the motion of the planets in the solar system. Now one of the
well known features of the solar system is that the planets further
out take longer to go around the Sun than planets nearer to
Sun. Translated to the galaxy this means that the rotation should be
faster in the inner parts of the galaxy than in the outer parts. As a
matter of fact this is not what is observed. Using the 21cm radiation
from neutral hydrogen that can be seen out to distances from the
centers of the galaxies where there are too few stars to see, Vera
Rubin measured the rotation speeds of galaxies out to extremely large
distances from their centers. And the rotation speed never reduced,
like it does in the solar system, in some cases it actually rose. This
lead to a quandary. Faced between accepting that Newton's
gravitational theory is incorrect and there is material that we cannot
see in any way other than by their gravitational pull on other matter,
we picked the easier choice. The resolution to the high rotation
speeds of spiral galaxies is to assume that there is material that
cannot be observed in light of any color (from 
-rays to radio
waves) but that exerts a gravitational pull on the stars and gas that
lie in a galaxy. This invisible matter is called dark
matter. This lead to a major revision of the masses of galaxies which
before used to be measured from the light the galaxy emitted. Now it
was anybody's guess as to how much mass that light signified. We are
now in a situation where possibly the material that we can see is only
a small fraction of the actual amount of matter in the Universe, most
of which is of a nature we cannot recognize.
There is a special group of galaxies that are peculiar and have thus attracted attention. It is believed that this peculiarity in all the cases has to do with events in the centers of the galaxies. One class of such galaxies is that of the Radio galaxies. These are galaxies that, as the name suggests, emit copious amounts of radio waves. The galaxy as seen in photographic plates look fairly average and innocuous. But when seen in radio waves they can be seen to have huge jets of material shooting out of the galaxy in opposite directions from the center of the galaxy. These jets emit light in radio waves. They appear to be plowing through some thin material even outside the galaxy that eventually manages to stop the jets which end in large lobes that are very bright in radio. The jets extend out many times larger than the visible galaxy and appear to extend in as close to the center as we can make out. Another group of such galaxies are the Seyfert galaxies. These are galaxies that appear normal except for a very prominent center. An extreme version of these are the Quasars, whose nucleus are so prominent that we only see their centers. These objects appear star-like in photographs. Hence their names (QUAsi-StellAr-Radio-Sources). They are also called Quasi Stellar Objects (QSO's).
In all these cases the culprit at the center is believed to be a blackhole. The reason to believe in their presence is manifold. For one these objects change their brightness in very short periods of time, months. For an object to change its brightness in a certain time the region producing the light must be smaller than the distance light travels in the time the object took to change its brightness. For something as bright as a galaxy to change its brightness in a month needs a very small source of incredible amounts of energy. The only plausible method of generating such energies in such a small volume is to have a blackhole that is gradually sucking up gas which radiates the energy as it struggles to stay out of the blackhole.
We've seen that stars are not distributed uniformly in the Universe but are collected in galaxies. Similarly it appears the galaxies are not distributed uniformly in the Universe. They are too collected in small groups or clusters that range from our local group with 10-15 galaxies (mostly small, aside from our own Milky Way and Andromeda) to the nearby Virgo cluster with over 1000 large galaxies. The clusters of galaxies on their hand group together to form superclusters. The superclusters of galaxies themselves lie in an ordered nature around the Universe. Small objects group together to form bigger objects, which collect together to form even bigger objects and so on towards bigger and bigger objects. This observation will turn out to be of great significance to Cosmology and the Universe later on.