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 learni) 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. TOC:Varieties.- Preschemes.- Local properties of schemes.- References.- Appendix:
Curves and their Jacobians.- Survey of work on the Schottky problem up to 1996 (by Enrico
Arbarello).- References.- Guide to the Literature and References (Curves and Their Jacobians).-
Supplementary Bibliography on the Schottky Problem.
