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The book consists of two parts. The first part describes new method of optimization that has the advantages at greater generality and flexibility as well as the ability to solve complex problems which other methods cannot solve. This method, called the "Method of Deformation of Functional (Extreme)", solves for a total minimum and finds a solution set near the optimum. Solutions found by this method can be exact or approximate. Most other methods solve only for a unique local minimum. The ability to create a set of solutions rather than a unique solution has important practical ramifications in many designs, economic and scientific problems because a unique solution usually is difficult to realize in practice. The second part of the book is devoted to applications of this method to technical problems in aviation, space, aeronautics, control, automation, structural design, and etc.