References
A classical introduction to the subject.
An overview of most basic "homotopical topics" as well as some more advanced categorical ones. For example one find can here an excellent general approach to homotopy (co)limits which balances on the fine line between being too general to the point of being unusable in calculations (Dwyer--Hirschhorn--Kan--Smith) and too concrete (like some AT books).
General philosophy of higher categories is discussed as well as the Grothendieck's program motivating this approach.
A slightly less classical text with more examples and harder emphasis on topos logic.
A very tedious and classical exposition of the topic. Although some times not easy to read. It is not uncommon to travel through several chapters in various parts of the book trying to track down some pesky lemma or definition.
Probably the best book about simplicial sets (with respect to the ratio details/size).
A classical yet modern exposition of a complex topic. The word of warning though: the book uses functorial factorization axiom throughout which makes it a bit different and incompatible with say Dwyer--Spalinski.
A purely point-free exposition of foundations of general topology.
An excellent introduction to a very flexible language of homotopical categories. That is relative categories with a nice 6-for-2 property. These objects are more convenient than model categories because there is no expectation of an intricate Fib-Cof structures, but they are still quite convenient for calculations.