This course introduces the students to the fundamental principles of continuum and applied mechanics, with particular emphasis put on the nonlinear mechanical behavior of matter. The course will cover tensor algebra/calculus, strain and deformation measures (both Lagrangian and Eulerian approaches), stress, conservation laws in solid and fluid mechanics, as well constitutive laws in elastic materials, Newtonian fluids, and viscoelastic solids. This course will be of particular interest to graduate students in Mechanical, Biomedical, Civil, and Geodesy and Geomatics Engineering, working in the fields of composites and nanostructured materials, biomaterials, stress analysis, finite element modeling, viscoelastic materials, computational fluid mechanics, etc.