This book investigates the implicit function paradigm, extending beyond classical theorems to encompass variational problems and solution mappings. The author, A. L. Dontchev, draws upon his expertise to present a unified collection of results, many of which are currently dispersed in the literature. The work begins with a foundational chapter on the classical implicit function theorem, suitable for undergraduate calculus students, before progressing to more advanced topics. Subsequent chapters explore implicit mappings defined by relations other than equations, with a particular focus on variational problems, and include applications relevant to numerical analysis and optimization.

The book is presented as a significant contribution to the field of analysis, aiming to become a standard reference. Its structure, moving from foundational concepts to advanced topics, suggests it is designed to serve a dual purpose: as a learning tool for students and as a comprehensive resource for researchers. The author's intent to unify existing results indicates a focus on providing a cohesive and accessible overview of the implicit function paradigm.