Milne's entire set of notes (algebraic number theory, class field theory, algebraic groups, complex multiplication, modular functions and modular forms, etc.), articles (abelian varieties, Jacobian varieties, Shimura Varieties, Tannakian Categories, etc.) and books (Elliptic Curves, Arithmetic Duality Theorems, Etale Cohomology etc.), available at www.jmilne.org/math/. They are indispensable for anyone who wishes to learn the fundamental concepts in arithmetic geometry. The Storrs lectures on Abelian Varieties and Jacobian Varieties are clear, succinct and give great references throughout. His notes on 'Class Field Theory' are superbly written. 'Etale Cohomology' is a standard reference for the subject, although I find his lecture notes on the same topic even more enjoyable. Finally, 'Arithmetic Duality Theorems' is quite possibly the only reference where one can find complete proofs of Tate's Duality Theorems as well as their generalizations using etale and flat cohomology.

1. Milne's entire set of notes (algebraic number theory, class field theory, algebraic groups, complex multiplication, modular functions and modular forms, etc.), articles (abelian varieties, Jacobian varieties, Shimura Varieties, Tannakian Categories, etc.) and books (Elliptic Curves, Arithmetic Duality Theorems, Etale Cohomology etc.), available at www.jmilne.org/math/. They are indispensable for anyone who wishes to learn the fundamental concepts in arithmetic geometry. The Storrs lectures on Abelian Varieties and Jacobian Varieties are clear, succinct and give great references throughout. His notes on 'Class Field Theory' are superbly written. 'Etale Cohomology' is a standard reference for the subject, although I find his lecture notes on the same topic even more enjoyable. Finally, 'Arithmetic Duality Theorems' is quite possibly the only reference where one can find complete proofs of Tate's Duality Theorems as well as their generalizations using etale and flat cohomology.

2. Part 4 (particularly Chapter XX) of Lang's 'Algebra'. I may have learned (as little as I have) about homological algebra from Weibel or Gelfund-Manin as texts, but I always keep coming back to Lang's exposition. Not a lot of motivation, but it covers almost everything you need to know in a first course.