Based on lectures presented by six internationally known experts at the 2002 MSRI introductory workshop on commutative algebra, this book focuses on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics. Six short papers describing work at the research frontier are also included. The unusual scope and format will make the book recommended reading for graduate students and researchers interested in commutative algebra applications.