This book is designed for students who have had no previous knowledge of the theory of heat conduction nor indeed of the general theory of partial differential equations. On the other hand, a degree of mathematical sophistication is assumed, in that the reader is expected to be familiar with the basic results of the theory of functions of a complex variable, Laplace transform theory, and the standard working tools involving Lebesgue integration. It should be understandable to beginning graduate students or to advanced undergraduates.