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I'm interested in learning homotopical algebra (by which I mean: model categories, simplicial methods, etc.) However, I've been unable to make heads or tails of any of the "standards" (Jardine&Goerss, Hovey, Hirschorn); they seem to presuppose knowledge of the subject material. What are some accessible introductions to this subject? (+ reading paths to get to the aforementioned "classics"?)

Background: I'm very comfortable with category theory and homological algebra, am learning enriched category theory, and have had a course in algebraic topology (and am currently studying more).

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    Also, I found the article by Goerss on the subject at http://jdc.math.uwo.ca/summerschool/ really fun. One application of the fact (explained in this article) that one can construct model structures on simplicial $R$-algebras for $R$ a commutative ring is the construction of the "cotangent complex": it is a nice concrete example of a (non-abelian!) derived functor.2011-09-15

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Have you tried to read Hirschhorn, but starting on Part 2? -The first part is the real purpose of the book -localization of model category structures-, but more specialized and advanced. The second part is designed to serve as a support of that, more advanced, first part, and contains all the basics of homotopy theory (model categories). I would try, at least, with chapters 7, 8 and 9 -see what happens: I think it's not intended to be a "pedagogical" book on model categories, but a reference for the results on the first part. Nevertheless it is, first of all, systematic, and secondly, quite readable.

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    I'm glad you're liking the second part. Don't forget Theo's advice: Dwyer and Spalinski is a great introduction. I particularly liked their very specific example about the necessity of deriving colim -and thus giving raise to hocolim.2011-09-21
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I don't know if it is quite an introductory book but Quillen is not bad at all.

Dwyer and Spalinski is good as well.

There is a section in the Motivic homotopy theory book written by Bjorn Dundas (the section is by Dundas, the whole book is by a few other people as well). This might give the overall picture before you look for something more detailed.

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    Maybe you should add this as a separate answer.2016-12-05