Basic references:

Peter May?, The geometry of iterated loop spaces (pdf)

Martin Markl?, Steve Shnider?, James D. Stasheff?, Operads in algebra, topology and physics, Math. Surveys and Monographs 96, Amer. Math. Soc. 2002.

nLab, operads

Examples of operads being used:

John Baez, John Foley?, Joseph Moeller, and Blake Pollard, Network models?, 2018. arXiv:1711.00037

J.-C. Aval?, S. Giraudo?, T. Karaboghossian?, and A. Tanasa, Graph operads, general construction and natural extensions of canonical operads?, preprint, 2020. arXiv:1912.06563