Continuum mechanics is widely taught to graduate students in applied mathematics, physics, and engineering, providing the basis for further study in fluid and solid mechanics. Presentations of the subject, however, vary greatly in their level of formalism, being either engineering and example oriented or mathematically over-sophisticated. Temam and Miranville provide a rigorous presentation of the underlying mathematics and physics of the problem, avoiding unnecessary use of function spaces. The authors then build on this base to present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics, including: viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This original text should be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level, whether in engineering, mathematics, physics, or the applied sciences.