This book is intended for advanced undergraduate and first-year graduate students in mechanical, aeronautical, and structural engineering and for those who deal with Theory of Materials. During the preparation of this book the principal objective has been to expose the mathematical framework as in detailed form as possible. The style and policy of teaching in the book has been in a form as it is delivered in the classroom. Separate chapters have been allocated for Elasticity, Thermoelasticity, and Viscoelasticity as well as two chapters for the Fluid Mechanics. Appendix B in Volume 2 contains rudiments of invariant representations of nonlinear constitutive tensor functions by the generators and integrity/function bases involved and an exposition of derivations of the constitutive equations for orthotropic, transversely isotropic, and isotropic elastic solids by use of structure tensors.