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For someone interested in algebraic geometry, the first chapters of Lipman's "Notes on Derived Functors and Grothendieck Duality", (in Foundations of Grothendieck Duality for Diagrams of Schemes, Lecture Notes in Mathematics, no. 1960, Springer, 2009) is a must. (And, btw. it is way better to read chapter 4 in this work for understanding Grothendieck duality than Harthorne's notes).