The highlighting of the fundamental simplicity of basic ideas and the breadth of their applications, as well as the systematic initiation of the reader into the use of symbolic programs for the study of Partial Differential Equations, are the main characteristics of this book. Special attention has been given to the organization of the material into clearly distinct parts - using internal "covers" - so that the book can serve both as a brief introduction to the subject (Part A) and as a comprehensive textbook for a full, semester-long course on Partial Differential Equations (Parts A, B, C). The main goal of the book is to provide Greek students of Natural Sciences and Polytechnic Schools with a modern education in differential equations that combines essential mathematical understanding with advanced skills in mathematical formulation and solution of realistic problems.