The book "Multivalued Analysis and Nonlinear Programming Problems with Perturbations" offers a comprehensive examination of the topological and differential properties of multivalued mappings and boundary functions. It specifically addresses the sensitivity analysis of optimization problems, focusing on nonlinear programming problems with perturbations. The developed methods are based on the theories and concepts of former Soviet researchers Demyanov and Rubinov, and many of the presented results are published in English for the first time. By using directional derivatives as a central tool for investigating nonsmooth functions and multifunctions, the book represents an advancement of quasidifferential calculus. Unlike other works in this field, particularly the recent publication by Bonnans and Shapiro, this volume analyzes the properties of boundary functions associated with optimization problems under general constraints defined by multivalued mappings. A unified approach to directional differentiability of functions and multifunctions forms the foundation of this volume.