The universe in which we live is a puzzling and unimaginably large place. It has been in existence for an incredibly long time and we humans are only able to observe it from a single point in space and time which makes it extremely difficult to understand and explain. It would be a bit like an intelligent microbe trying to work out the detailed structure of the human body from a single point inside of a bone! Cosmology is the name given to the study of the origin and nature of the universe and there have been many theories developed, ranging from creation by an all-powerful being to the currently accepted scientific explanation we call the Big Bang.
Possibly the most important moments in the history of cosmology were when Einstein came up with his two theories of relativity.
Within about 20 years or so, scientists had realized that the universe was expanding at an enormous rate. Using a device called a spectrometer (a device that splits light into its component wavelengths), an astronomer called Vesto Slipher had observed the phenomenon of redshift. He did this because every star and galaxy has certain dark lines on its spectrum. He noticed that when he took the spectrum of distant galaxies, these lines were not in their normal positions, they were always displaced towards the red part of the spectrum. The significance of this was identified by another astronomer, Edwin Hubble. He looked carefully at Slipher's findings and realized that the further away the galaxy was, the greater the redshift. Whilst Hubble was doing this, a Belgian, Georges Lemaitre, had worked out that the universe should be expanding using Einstein's theories. His ideas were the start of what was to be called the Big Bang theory.
Redshift arises because of the Doppler effect. As an object recedes from an observer (or vise versa), any waves leaving the object will be changed by the motion. The crests of successive waves are emitted slightly further away than if the object was stationary and so they have a longer wavelength (and therefore lower frequency). You can think of the movement as stretching the waves. For light, longer wavelengths mean redder light, hence the name redshift.
Explaining the expanding universe gave rise to several theories, the two most favored ones were the Steady State and the Big Bang. In science, when a theory is put forward, it is then tested. This is done by making predictions and then testing the prediction. One of the predictions of the Big Bang theory was that there would be an 'echo' of the massive explosion that created our universe, the cosmic microwave background radiation. This was discovered in 1964.
Another prediction of Einstein's theories is the existence of black holes. These are the remains of massive stars that have run out of nuclear fuel and collapsed in on themselves under the influence of gravity. They are so compact that their gravitational attraction is enormous, not even light can travel fast enough to escape it so they can't actually be seen directly. There is still no definite proof that these strange objects exist but scientists are looking for evidence. This is done in several ways. Matter falling into a black hole will be heated to such high temperatures that it will emit high energy radiation like X-rays just before it enters the black hole. Objects near to a black hole would be affected by its gravity so astronomers are looking for objects which appear to be orbiting something that they can't see. The gravity of a black hole is so great that it can bend light, exactly the same as a lens does. This is called gravitational lensing and astronomers are looking for this too. One of the latest ideas is that at the center of many galaxies, including our own, there is a super-massive black hole pulling the stars in towards itself.