This book gives a detailed account of recent work on relations between commutative algebra and intersection theory, with a particular emphasis on applications of the theory of local Chern characters. This theory is the result of many years of development, having originated in topology and been introduced in algebraic geometry about thirty years ago. Building on the algebraic form described in Intersection Theory by W. Fulton, Paul Roberts presents further developments and important algebraic applications that were not known at the time Fulton's book was written. Students and researchers specializing in commutative algebra will find access to a wide range of new ideas in this book.