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. The work presents a large quantity of results previously scattered throughout the literature. This volume is a first introduction to this rapidly developing subject, but will also be useful as a 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.