This unique reference is the first book of its kind to give a complete and rigorous presentation of the mathematical study of the expressions-hemivariational inequalities-arising in problems that involve nonconvex, nonsmooth energy functions. Establishing a theory of the existence of solutions for inequality problems involving nonconvexity and nonsmoothness, Mathematical Theory of Hemivariational Inequalities and Applications illustrates new mathematical results with examples from mechanics, engineering, and economics examines the structure of functions whose generalized gradient is pseudo-monotone, generalized pseudo-monotone, or quasi-pseudo-monotone introduces a directional growth condition that permits the derivation of new existence results for discontinuous variational problems in nonreflexive vector-valued function spaces describes a model of delamination in which noncoercivity occurs develops efficient, novel methods for the treatment of noncoercive problems provides never-before-published existence results for constrained problems for nonconvex, star-shaped sets and more!