Microlocal analysis has been a fast developing field. In this book, the authors publish their research results in a summarized form. They deal with the following themes: asymptotic solutions for several classes of linear PDO with multiple characteristics; applications to microlocal solvability and hypoellipticity of the same classes of operators; solvability and hypoellipticity on the torus including construction of global parametrices; applications of the asymptotic methods and Gevrey microlocal analysis to the billiard ball map; and a survey of results in the domain of hypoellipticity and solvability in connection with the construction of asymptotic solutions.

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."..the authors are able to record the considerable progress realized recently in the field...topics have been chosen so that the reading is both attractive and useful, for experts and non-experts."(Mathematical Reviews Issue 2001g)

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