Abstract: In this seminar, I will introduce the Kac-Moody group associated with a Cartan matrix, then how to construct the homotopy colimit of classifying spaces of parabolic subgroups directly. Theoretically, we can know the classifying space of a Kac-Moody group from the previous homotopy colimit. I will apply that method to detailed computation of integral cohomologies of those classifying spaces with cases of exceptional Lie groups and projective unitary groups, in which spectral sequences are widely used.