The book "Connectedness and Necessary Conditions for an Extremum" by A. P. Abramov offers a comprehensive introduction to the application of topological connectedness as a fundamental tool for investigating necessary conditions for extrema. It is the first work to integrate these concepts in the theory of maxima and minima so thoroughly. The author adopts a relatively elementary style and has made an effort to make the book as self-contained as possible, assuming basic knowledge in topology, functional analysis, and optimization theory. The synthesis of the well-known Dybovitskii-Milyutin methods with topological approaches allows for the presentation of new results in optimization theory and offers a non-standard perspective on classical results. The book is aimed at applied mathematicians and students interested in the theory of optimization and its applications.