The theory of differential graded algebras (in char 0) and their modules has numerous applications in rational homotopy theory as well as algebraic geometry.
I'm looking for a reasonably complete reference book/collection of articles that treat the basic algebraic and homotopical aspects of dg-algebras akin to Atiyah-MacDonald's book on commutative algebra.
Hopefully containing the following topics
- Model structures on dg algebras and simplicial algebras (presenting the "correct" infinity category) and relation between them (concrete description of fibrations and cofibrations).
- Resolutions and minimal models
- Localizations and Completions
- Analogs of the classical types of morphisms (flat, smooth, unramified, etale, open immersion, closed embedding, finite, finite type, etc.).
- Derived categories of modules (Triangulated / Stable $\infty$) and functors on them (push-pull-shriek functors, perfect complexes vs. bounded vs. unbounded derived categories, dualizing complex, cotangent complex, localization and completion, fourier mukai transforms).
- Derived descent theorems - descent for dg-modules in the derived categories. (hopefully making it clear what kind of information goes into glueing a dg-module).
- Hochshild and Cyclic (co-)homology
- DG lie algebras and Koszul duality
I realize that one can always go to Lurie's books for a comprehensive and much more general treatment but I hope that a more elementary reference exists. I do believe that some aspects of this theory are a lot less technical than they appear.