This is a first-year graduate textbook on linear elasticity, based on a one-semester course taught by the author at the University of Michigan. It is written with the practical engineering reader in mind, with dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Most of the text should be readily intelligible to a reader with an undergraduate background of one or two courses in elementary strength of materials and a rudimentary knowledge of partial differentiation. Throughout, emphasis is placed on engineering applications of elasticity and examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results. The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems. Problems suitable for class use are included at the end of most of the chapters. These are expressed wherever possible in the form in which they would arise in engineering - ie as a body of a given geometry subjected to prescribed loading - instead of inviting the student to "verify" that a given candidate stress function is appropriate to the problem. The text is therefore written in such a way as to enable the student to approach such problems deductively.