There is a great introduction by May, "The Geometry of Iterated Loop Spaces". I really enjoy reading it, but it was written 50 years ago and contains outdated technical details related to the language of topological spaces. Now, as far as I understand, there is no doubt that this should be stated in the language of simplicial sets. What are the best references nowadays? I found, for example, Simplicial and Operad Methods in Algebraic Topology. Is this a good introductory text?

In this question, I am interested in operads specifically in homotopy theory, in particular, the connection with iterated loop spaces (so the question about algebraic operads is not relevant to the current topic, as far as I understand, although the algebraic theory of operads also fascinates me).

certainly betterbecause they already form a topos (this seems to be exactly what the technical requirements like CGWH are aiming for). My friends and I are planning a seminar on operads this fall, and I wanted to avoid (what I thought) outdated math crutch in the program. $\endgroup$3more comments