Roger Fosdick The Journal of Elasticity: The Physical and Mathematical Science of Solids invites expository articles from time-to-time in order to collect results in areas of research that have made significant impact on the field of solid mechanics and that show continued interest in present-day research and thinking. The Stroh formalism is one such area, especially as it impacts upon the analysis of anisotropic media, that has been generalized from linear elastostatics to cover linear theories of piezoelectro-elasticity and megneto-elasticity as well as elastic wave phenomena. In this work, Kazumi Tanuma presents the essential elements of the Stroh formalism, its major theorems with proofs and applications, in a research-level textbook form. The presentation is self-contained and the development is clear and concise. Professor Tanuma efforts to produce a straightforward, accurate and readable account of this subject are clearly evident. He has organized the subject with a common logical thread throughout and he has given basis for not only the importance of this area of research, but, most importantly, for understanding its meaning and significance.