Offers an introduction to abstract algebraic geometry. This book enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed to answer these questions.

Provides an introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. This book studies the case of elliptic curves, and concludes with the fundamental theorem of stable reduction of Deligne-Mumford.

Presents a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality. This book describes Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it.

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric.

Algebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion of algebraic geometry. This book provides a foundation to proceed to advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves.

All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.