This book is intended to be a self-contained introduction to the theory of composite materials, encompassing the electrical, thermal, magnetic, thermoelectric, mechanical, piezoelectric, poroelastic, and electromagnetic properties. It is intended not only for mathematicians, but also for physicists, geophysicists, material scientists, and electrical and mechanical engineers. Consequently, the results are not stated in the format of lemmas, propositions, and theorems. Instead, the focus is on explaining the central ideas and providing proofs that avoid unnecessary technicalities. The book is suitable as a textbook in an advanced-level graduate course, and also as a reference book for researchers working on composites or in related areas.

The field of composite materials is enormous. That's good, because it means that there are many avenues of research to explore. The drawback is that a single book cannot adequately cover the whole field. The main focus of this book is on the relation between the microstructure of composites and the effective moduli that govern their behavior. This choice reflects my research interests, and is also the starting point for many other avenues of research on composites.