This book is suitable for a first-year graduate course on Non-linear Elasticity Theory. It is aimed at graduate students, post-doctoral fellows and researchers working in Mechanics. Included is a modern treatment of elementary plasticity theory emphasizing the foundational role played by finite elasticity. The book covers fundamental and advanced material that should be mastered before embarking on research. Included are the concepts of frame invariance, material symmetry, kinematic constraints, a development of nonlinear membrane theory, energy minimizers as stable equilibria and various attendant convexity conditions.