This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and provides an easy approach for readers to understand. Contents:Existence Theorems for Cauchy ProblemsExistence Theorems for Evolution Equations (I)Linear Autonomous Parabolic EquationsNonlinear Autonomous Parabolic EquationsLinear Non-autonomous Parabolic EquationsNonlinear Non-autonomous Parabolic Equations (I)The Associated Elliptic EquationsExistence Theorems for Evolution Equations (II)Nonlinear Non-autonomous Parabolic Equations (II)AppendixReadership: Mathematical graduate students and researchers in the area of Analysis and Differential Equations. It is also good for engineering graduate students and researchers who are interested in parabolic partial differential equations.