This book presents the basic concepts for the mathematical modeling of classical solid and fluid continuous media. It consists of eight chapters treating, Cartesian tensors, the kinematics, and dynamics of a continuous medium, thermodynamics, constitutive equations of classical Newtonian fluids and elastic solids, introduction to the linear theory of elasticity as well as Newtonian fluid mechanics. In each case, simple application examples provide analytical solutions that illustrate the power of modeling using continuum mechanics principles. Appendices give the necessary additions to follow the work and represent the field equations in cylindrical and spherical coordinate systems. Each chapter proposes a series of exercises and suggestions for their solution is also provided. Clear and educational, this book is intended for engineering and physics students who want to learn the basic principles of continuum mechanics. The subject is developed in a simple-to-follow pedagogical manner that readers can work through on their own. They will find in this work a complete modern introduction that opens the door to this vast territory of knowledge.