The book "Finite Element Method for Hemivariational Inequalities" offers a comprehensive and rigorous analysis of the finite element approximation for a specific class of hemivariational inequalities that are significant in non-smooth and non-convex mechanics. It addresses problems that can be formulated with non-monotone, possibly multi-valued, constitutive laws. The authors describe the finite element models and their convergence properties, while the discretized models are treated as non-convex and non-smooth optimization problems. The book is aimed at engineers and applied mathematicians working in industry or academia, as well as graduate students engaged in advanced nonlinear computational mechanics and the mathematics of finite elements. It is self-contained and includes all the necessary fundamentals from the fields of finite element mathematics, functional analysis, and non-smooth analysis, which are summarized in the introductory chapter.