The purpose of the this book is to put together in one place the basic elementary techniques for solving problems in maxima and minima other than the methods of calculus and linear programming. The emphasis is not on individual problems, but on methods that solve large classes of problems. These methods are organized in terms of the mathematical ideas used, whether from algebra, geometry, the theory of inequalities, and so on. The many chapters of the book can be read independently, without references to what precedes or follows. Besides the many problems solved in the book, others are left to the reader to solve, with sketches of solutions given in the later pages.