This book is designed for use by students and teachers in the field of applied mechanics and mathematics, and for practitioners in civil and mechanical engineering. Since tensor calculus is an indispensable prerequisite when dealing with the theory of elasticity in a modern way, the first part of the book consists in an introduction into this subject. In the second part, the physical foundations of the theory of elasticity are given, including nonlinearities. The excursion into the field of geometric and physical nonlinearities is done in order to prepare the reader for further advances into the most recent developments of the theory. The book itself, in the remainder, is restricted to linear problems only. The third part of the book deals with the mathematical theory of linear elasticity in full extent. Curvilinear problems, two- and three-dimensional problems are included. Stress has been put on working out a systematic approach to the solutions of all kinds of stress states, not neglecting triaxial problems. Also, energy methods have been dealt with, taking into account the generalization and extension of these methods by Rudiger and Reiss ner. The fourth and last part of the book consists in an application of the general methods, as outlined in part 3, to special structures like plates and shells, thus giving hopefully something of interest to the practising engineer.