"The University allows you to research new technologies to make your city more efficient and your military more powerful."-Global Warfare.
The university uses up 120 food, 1,500 stone, 2,500 oil, and 200 steel to build. You need to be level 2 to build it. It takes 15 seconds to build. You can research stuff with it. Better researches need more stuff done first (higher level University, other researches first). Unless the University level needed for the research type is higher than the level you are researching, university level=highest level researchable.