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The book contains a collection of formulas for Mathieu functions in a uniform notation for these functions, and also a description how these functions can be generated numerically. An example shows the use of Mathieu functions in a class of physical problems. The book contains lists of numerial values and diagrams of the functions, as well as a print of computer programs for Mathieu functions. A disk with these programs is added. Readership: Mathematicians - Physicists - Engineers