Explore the foundational theory of differential identities in associative rings and algebras with this comprehensive monograph. This essential resource delves into identical relations involving arbitrary elements and differential functions within rings and algebras, offering a powerful tool for solving complex problems. Discover its extensive applications in invariant theory, non-commutative geometry, mathematical physics, and advanced ring theory, particularly in resolving 21st-century challenges. This book, ideal for researchers in differential identities, synthesizes three decades of advancements. It covers various derivations, including generalized, skew, and b-generalized types, explores their properties, and examines their interaction with rings and algebras with involution. Delve into the characterization of higher derivable mappings and the structure of Lie and Jordan-type higher derivations, with a dedicated chapter on applications. Authored for researchers seeking an authoritative overview of differential identities in rings and algebras.