This comprehensive textbook/reference focuses on the mathematical techniques and solution methodologies required to establish the foundations of anisotropic elasticity and provides the theoretical background for composite material analysis. Specific attention is devoted to the potential of modern symbolic computational tools to support highly complex analytical solutions and their contribution to the rigor, analytical uniformity and exactness of the derivation. It will appeal to a broad audience possessing good mathematical skills and involved in mathematical modeling, including: graduate students and professors, applied mathematicians, numerical analysts, scientists, engineers, and researchers.