Mumford D. The Red Book of Varieties and Schemes 2ed 1999

Textbook in PDF format

Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all about.
This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry. The book is aimed at graduate students and professors seeking to learn
i) the concept of "scheme" as part of their study of algebraic geometry and
ii) an overview of moduli problems for curves and of the use of theta functions to study these.
Varieties
Preschemes
Local Properties of Schemes
Appendix: Curves and Their Jacobians
References: The Red Book of Varieties and Schemes
Guide to the Literature and References: Curves and Their Jacobians
Supplementary Bibliography on the Schottky Problem