This book offers the first systematic presentation of the theory of the mixed problem for hyperbolic differential equations with variable coefficients. This class includes hyperbolic and parabolic equations as well as nonclassic type of operatorthe \(q\)hyperbolic equationwhich was introduced by the authors. As part of the exposition, the authors consider the Cauchy problem for this class of equations. This book would be suitable as a graduate textbook for courses in partial differential equations. Readership Graduate students and research mathematicians working in partial differential equations. Reviews "The book ... has advantages which make it distinctive ... gives a good introduction to the subject, and can be understood by undergraduate students ... an expert may well find many useful technical results and observations that were previously unknown."  Bulletin of the London Mathematical Society Table of Contents  Basic classes of polynomials
 The Cauchy problem
 Mixed problem for hyperbolic equations
 Mixed problem for \(q\)parabolic and \(q\)hyperbolic equations
 References
 Notation index
 Subject index
