This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject. Divided into two parts, in the first part readers already well- acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green¿s function, and Green¿s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single- layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic,