"Approximate Commutative Algebra" is a scholarly book that addresses an emerging research area bridging the gap between traditional exact computation in commutative algebra and approximate numerical computation. Over the past five decades, exact computation in commutative algebra has made significant advances. Given the central role of polynomials in scientific modeling, it is only logical to extend these concepts to the processing of approximate, empirical data derived from physical measurements of real phenomena. In this volume, nine contributions from established researchers present various approaches to solving a wide range of problems that arise in the context of Approximate Commutative Algebra.