Fundamentals of continuum mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. * uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics* covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures* offers a unique approach to modeling incompressibility and thermal expansion, based on the authors' own research.