This textbook provides a rigorous yet accessible introduction to Nonlinear Elasticity aimed at undergraduate students in a compact text. Rooted in concepts from first- and second-year undergraduate Linear Algebra and Calculus (and very little Tensor Algebra), the book touches upon all the fundamental aspects of nonlinear elasticity, from the analysis of deformation and stress, to the constitutive response and modelling of soft solids, to the lab experiments required to obtain their material properties, and to the concepts of equilibrium and energy minimization. Nonlinear Elasticity is an elegant, physics-based, mathematical theory, one usually only available at graduate level to students in advanced studies of engineering, applied mathematics, and theoretical physics. Over the past ten years, the authors developed a classroom-tested pedagogy aimed at narrowing the range of the skills required to approach Nonlinear Elasticity from the perspective of an undergraduate student pursuing a Bachelor of Science or Engineering, as displayed in this book. It concludes with an analysis of several worked examples, spanning a variety of problems of high technical importance and relevance. The book is organized for use as a core text in the classroom or as a self-contained guide of (24 lectures) for independent learning.