Since Bose and Einstein discovered the condensation of Bose gas, which we now call Bose-Einstein condensation, its mathematical properties have been of great importance for mathematical physics. Recently, many rigorous results have been obtained, mostly about its ground state energy and its dynamics in various models. In this talk, mathematical frameworks to study Bose gas will be introduced. Heuristics arguments and proofs to understand the properties of Bose gas will also be explained.