Rings and ideals
Modules and algebras
Polynomial and power series rings
Homological tools I
Tensor, symmetric and exterior algebras
Finiteness conditions
Primary decomposition
Filtrations and completions
Numerical functions
Principal ideal theorem
Integral extenstions
Normal domains
Transcendental extensions
Affine algebras
Derivations and differentials
Valuation rings and valuations
Homological tools II
Homological dimensions
Depth
Regular rings
Divisor class groups

Suitable for a one or two semester course in commutative algebra, this textbook provides an introduction to commutative algebra at the postgraduate and research levels.