Someone asked about how the "edge" of the universe is defined. It is defined by the end of spacetime. Spacetime is the "stuff" the universe is made of. It is expanding, or rather, stretching may be a better word. And it's carrying all the matter/energy along with it. The distant galaxies we see aren't really moving away, actually. The space in between them is growing larger.
This "expansion" is caused by something we do not understand that we're currently calling "dark energy." It works by stretching spacetime, the converse of gravity, which contracts spacetime. Locally, where matter is close together, gravity is stronger than dark energy. Hence the formation of galaxies, stars, planets, etc. But the spaces in between galaxies are far more vast than the galaxies themselves, so dark energy is stronger in those spaces, and galaxies insufficiently close for gravity to overcome dark energy, are moving apart.
There is only one galaxy, besides are few close small satellite galaxies, which is close enough to be moving towards us: Andromeda. It will collide with our galaxy in a billion or so years. All other galaxies in the universe are moving farther away.
The way the red shift works is, when electromagnetic radiation, i.e. what we call "light" and all wavelengths longer and shorter, moves through the universe, the dark energy that stretches spacetime is stretching the radiation along with it. Think of a string arranged as an up and down wave. What happens when you pull the string from both ends?
The frequency of the wave decreases, the wavelength increases, and the amplitude of each waves shortens. Hence, light shifts toward the red (low frequency) end of the spectrum as it moves through expanding space. Eventually it will be a radio wave, then nothing, once the "string" is pulled taught.
Light travelling short distances, however, through galaxies where gravity is stronger than dark energy, shifts towards the blue end of the spectrum.