this monograph is devoted to krull domains and its invariants. the book shows how a serious study of invariants of krull domains necessitates input from various fields of mathematics, including rings and module theory, commutative algebra, k-theory, cohomology theory, localization theory and algebraic geometry. about half of the book is dedicated to so-called involutive invariants, such as the involutive brauer group, and is essentially the first to cover these topics. in a structured and methodical way, the work presents a large quantity of results previously scattered throughout the literature. audience: this volume is recommended as a first introduction to this rapidly developing subject, but will also be useful as a state-of-the-art reference work, both to students at graduate and postgraduate levels and to researchers in commutative rings and algebra, algebraic k-theory, algebraic geometry, and associative rings.