Mechanics of solids as theories of Elasticity and Plasticity and the theories of fluid flows were developed centuries ago, but their combined constitutive filed theory appeared only in recent six decades. During its evolution as Continuum Mechanics, the approach was somewhat obscure compounded by obscure tensorial notations. Clearer versions of the theory appeared subsequently and at present standardization has been reached with the use of Cartesian tensors that are closely related to matrices. This text gives a clear presentation of this formalism of Continuum Mechanics that can be applied to not only classical solid and fluid mechanics, but shows the way to newer materials that are increasingly finding technical applications. The book will thus be useful as text for M.Sc. and M.Tech. students, and also researchers on mechanics of continuous materials of different varieties.