I read a very user-friendly and modern treatment of closed model categories in Homotopy theories and model categories by Dwyer and Spalinski and I liked it very much. This basically covers Chapter I of Quillen's Homotopical Algebra.
I was wondering if there are modern treatments of chapter II, i.e. are there any user-friendly modern exposition on simplicial homotopy theory? The more similar to Dwyer and Spalinski's the better. Thank you!
Try Goerrs and Jardine's Simplicial Homotopy Theory.