For a good survey of modern physicists’ understandings of the universe, see Columbia University professor Brian Greene’s book, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, Vintage, 2005.
For an in-depth overview of the picture of the universe that has grown out of Albert Einstein’s theories, read CalTech professor Kip Thorne’s book, Black Holes and Time Warps: Einstein’s Outrageous Legacy, WW Norton & Company, 1995.
To understand the radical re-imagining of the universe in relativity theory, it may help to investigate earlier models. Here’s an overview from the Australian national science agency, CSIRO.
A good overview of Einstein’s thinking, with animations, can be found at this page from the University of New South Wales, by physics professor Joe Wolfe. http://newt.phys.unsw.edu.au/einsteinlight/
More information about Albert Einstein, his work, and modern research in relativity is available at Einstein Online, presented by the Max Plank Institute for Gravitational Physics. http://www.einstein-online.info/
Read about Albert Einstein’s life and work at this biographically rich site, presented by the American Institute of Physics.
John Norton, professor at the University of Pittsburgh, explains Einstein’s thought experiment on chasing a beam of light.
More on Einstein’s work and thinking by Norton can be found here: http://www.pitt.edu/~jdnorton/Goodies/
Einstein’s ideas on relativity have been tested through numerous experiments. You can get a quick overview from NASA here:
Or visit this webpage by physicist Tom Roberts, hosted at the Mathematics Department of the University of California, Riverside, for a great amount of detail: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
The effects of relativity can be hard to see, but understanding the phenomenon has some practical uses, such as in running the Global Positioning Satellite system. A reader-friendly description by C. Renée James, professor at Sam Houston State University, can be found here: http://blogs.discovermagazine.com/crux/2014/08/29/like-gps-thank-relativity/#.VAXei2Sqopw
Get a sense of the size of the universe by following this guide to a trip at the speed of light, by professor Gene Smith, from the University of California, San Diego. http://casswww.ucsd.edu/archive/public/tutorial/Intro.html
Explore images and 3D maps based on research from the Sloan Digital Sky Survey here: http://www.sdss.org/
Students can also classify galaxies at the Galaxy Zoo. http://www.galaxyzoo.org/