This book describes in detail a series of new strategies to solve problems, mainly in mathematics. New techniques are presented which have been tested in class by the author for over thirty years. These techniques advance the state-of-the-art in problem solving and extend existing methods of such great mathematicians and cognitive psychologists such as G. Polya, H.A. Simon, W. Wickelgren, and J. Greeno. The book provides each technique with a detailed description and then illustrates it through a number of problems spanning a wide spectrum of mathematical areas.