The topological approach to understanding the moduli space of curves is partly built upon the language of basic stable homotopy and infinite loop spaces, so it is probably wise to know at least a little about the language of infinite loop spaces. The book of Adams [Ada78] is highly readable and its first few chapters are certainly the place to begin. For the relation between monoidal categories and infinite loop spaces, Segal's original two papers [Seg68] and [Seg74] make for good reading, and May's paper [May74] states the theorems of the subject nicely.

Jeffrey Herschel Giansiracusa 2005-06-27