It's obvious that the Universe is big, so big that our common metrics of inches, feet, and miles are simply impractical for astronomical measurements. One metric is the astronomical unit (AU), the average distance between the Earth and the Sun (93 million miles). Most commonly, astronomers use lightyears, which is the distance light travels in a year (roughly 6 trillion miles). There's another metric called the parsec that's sometimes used, so I'll define it in the diagram below

Given a right triangle where the shorter leg is 1 AU and the opposite angle is 1 arcsecond (1/3600th of a degree), the other leg (the green line) is equal to one parsec. As it turns out, one parsec = 3.26 light years

The nearest star to us is Proxima Centauri, a little red dwarf 4.2 light years away. 

Our solar system is located in one of the spiral arms of the Milky Way, far away from the center. The Milky Way is about 100,000 light years wide. We all know the Earth takes one year to revolve around the Sun, but did you know the Sun takes 230 million years to make one complete revolution around the Milky Way (a galactic year)?

A hundred years ago, people thought the Milky Way was the extent of our Universe; they didn't know other galaxies existed. But in the 1920s, Edwin Hubble not only discovered other galaxies, but he also noticed the curious observation that every galaxy he observed was moving away from us.

Why is this strange? If galaxies moved through the Universe in random fashion, we'd expect to see some moving towards us and some moving away. His observations can only be explained if the Universe itself is expanding. Consider the analogy of the expanding balloon:

If the Universe is this balloon and we live on the surface of it, then as the Universe expands, from any vantage point it appears that everything else is receding away from you. This also answers the question of where the center of the Universe is. The center of the Universe is in a higher dimension. In the analogy of the balloon, we'd live in a 2D world and the center of the Universe is in the third dimension. In the real world, just take everything up one dimension - we live in a 3D world and the center of the Universe is in the 4th spatial dimension.

Red Shift / Blue Shift

How did Hubble know the galaxies he saw were moving away from us? Galaxies are made of stars, and stars are made of hydrogen and helium. Every element gives off a unique emission spectrum caused by energized electrons bouncing from higher to lower energy states and emitting photons (recall the concept of quantization). 

We can experimentally determine the stationary emission frequencies of hydrogen and helium in the lab, then compare to what we observe from distant galaxies. The high velocity of galaxies moving away from us creates a Doppler effect that results in a redshift in the observed frequencies in the emission spectra of other galaxies (if a galaxy were to move towards us, we'd see a blueshift)

Notice how on the above emission spectra, the further away a star is, the greater the redshift. Hubble quantified this relationship through Hubble's Law:

$v = H_0d$

$v =$ recession velocity in km/s

$H_0 =$ Hubble constant (approx. 67.7 km/s/Mpc)

$d =$ distance in Megaparsecs

Einstein was thrilled at the news that the Universe is expanding. His theory of general relativity was accurately quantified in a set of equations called the Einstein Field Equations (check them out here, they're beyond me!), but these equations did not allow for a static Universe. It had to be either expanding or contracting. Thus, Einstein included a "cosmological constant" term that would force the Universe to be static, but he couldn't figure out an explanation for it. With this new discovery, Einstein could remove this term. He later called it the biggest blunder of his life 

Based on the observed expansion of the Universe and the Cosmic Microwave Background (CMB, discussed below), we can demonstrate that the Universe must have originated at a single point that for some reason began rapidly expanding 13.7 billion years ago. This expansion is the Big Bang

In the brief instant after the Big Bang, the Universe was just a small and immensely hot ball of energy. But as the Universe expanded and cooled, matter condensed out of the energy and formed the galaxies and everything we see today

The CMB is the radiation that permeates the Universe as a leftover from the Big Bang. The space between the stars and galaxies appears dark, but a sensitive radio telescope shows a faint glow in all directions. 

It was first theorized in 1948 but was discovered by accident in 1965 when two researchers at Bell Telephone Laboratories were creating a radio receiver, and they kept on picking up this background noise that was coming uniformly across the sky. This was suspicious because most light sources radiate away from a point.

During the first 380 thousand years of the Universe, the background temperature was too hot for hydrogen atoms to form; instead, protons and electrons formed an opaque hydrogen plasma. This period of the Universe was called the "Dark Ages" because if something is opaque, it scatters photons. But when the Universe cooled enough for atoms to form, the Universe became transparent for the first time, allowing photons to travel freely and propagate the Universe. These leftover photons are the CMB.