From categories to homotopy theory Basic notions in category theory Natural transformations and the Yoneda Lemma (Co)limits Kan extensions Comma categories and the Grothendieck construction Monads and comonads Abelian categories Symmetric monoidal categories Enriched categories Simplicial objects The nerve and the classifying space of a small category A brief introduction to operads Classifying spaces of symmetric monoidal categories Approaches to iterated loop spaces via diagram categories Functor homology Homology and cohomology of small categories.