Reference request for functorial approach to classifying spaces

Question

In the introduction to Bott and Tu's Differential Forms in Algebraic Topology, there was mention that

...there was no time left within the scope of our book to explain the functorial approach to classifying spaces in general and to make the connection with the Eilenberg--MacLane spaces.

Is there a good reference that has covered this material?

Answer 1

One source is Algebraic Topology by Tammo Tom Dieck, section 14.4.