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.