I have studied the Milnor's construction of classifying spaces for classifying vector and principal bundles from the book 'Fibre Bundles' by Dale Husemoller. However this book does not discuss the cohomology of $BG$ & $EG$. Could someone please suggest some good reference for understanding cohomology of classifying spaces ? At the present instant, I am interested in knowing why the odd cohomology of the classifying space vanishes.
Thanks