This book is designed to present the fundamental concepts of electromagnetic field theory as they relate to modern engineering applications. As an up-to-date reference it can be used by practicing engineers, or as a text/supplement in standard university courses in electromagnetics or electromagnetic fields theory. The book has been designed for self-study with a problem-solving approach. Numerous examples with complete, worked-out solutions guide the reader through the concepts under discussion. Beginning with a review on vectors and coordinate systems, the book covers basic Coulomb's law in vector form up through the propagation of the electromagnetic wave in wave guides. Maxwell's equations which form the central theme are developed from the historical approach wherein relevant experimental laws are gradually introduced and manipulated with the help of steadily increasing knowledge of vector calculus. These equations are identified as and when they occur for static and time varying fields. In the last two chapters these equations are then explored in a collective way.