Analytic Methods in the Theory of Differential and Pseudo Differential Equations of Parabolic Type The theory of parabolic equations a well developed part of the contemporary theory of partial differential equations and mathematical physics is the subject of immense research activity. A stable interest to parabolic equations is caused both by the depth and complexity of mathematical problems emerging here and by its importance in applied problems of natural science technology and economics. This book aims at a consistent and as far as possible complete exposition of analytic methods of constructing investigating and using fundamental solutions of the Cauchy problem for the following four classes of linear parabolic equations: 2b parabolic partial differential equations in which every spatial variable may have its own weight with respect to the time variable degenerate partial differential equations of Kolmogorovs structure which generalize classical Kolmogorov equations of diffusion with inertia pseudo differential equations with non smooth quasi homogeneous symbols fractional diffusion equations. All of these provide mathematical models for various diffusion phenomena. In spite of a large number of research papers on the subject this is the first book devoted to this topic. It will be useful both for mathematicians interested in new classes of partial differential equations and physicists specializing in diffusion processes