There is a great introduction by May, "[The Geometry of Iterated Loop Spaces](https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.170.2840&rep=rep1&type=pdf)". I really enjoy reading it, but it was written 50 years ago and contains outdated technical details related to the language of topological spaces.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](https://bookstore.ams.org/mmono-198). 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](https://mathoverflow.net/questions/139021/good-reference-for-studying-operads) about algebraic operads is not relevant to the current topic, as far as I understand, although the algebraic theory of operads also fascinates me).



How now to study operads in homotopy theory?
One of the most comprehensive references today is certainly:



> 
> B. Fresse, *Homotopy of Operads and Grothendieck–Teichmüller Groups*, Mathematical Surveys and Monographs 217. <https://bookstore.ams.org/surv-217/>
> 
> 
> 


However, the idea that topological spaces are obsolete and that we should only use simplicial sets is a bit misguided. How do you define a manifold using just simplicial sets? Or the little disks/cubes operads? Simplicial sets of course have their place, but there are times when you just can't avoid topological spaces.


