This book in its entirety (both volumes) is intended to give a mathematical introduction (at the graduate level) to the axioms and laws of deformable body mechanics, and its various applications such as in the fields of solid and fluid mechanics. This textbook aims to present a comprehensive view of the whole subject starting from the elements of tensor analysis, which is the mathematical underpinning of this subject, then moving on to a detailed derivation of the governing equations, and then finally presenting very detailed applications in the areas of linear and nonlinear elasticity, and fluid mechanics. This emphasis on both theory and applications is reflected in the title "Foundations and Applications of Mechanics." The book tries to be as self-contained as possible. Thus, detailed proofs for almost all the results have been given in the introductory chapter on tensors, rather than referring the reader to other books or papers. In the second volume on fluid mechanics, a detailed summary of the governing equations which have been derived in the first volume has been presented to facilitate the reader.