The theory of variational inequalities is a relatively young mathematical discipline. One of the bases for its development was the contribution of Fichera [5], who coined the term “Variational Inequality” in his paper on the solution of the frictionless contact problem between a linearly elastic body and a rigid foundation posed by Signorini [15]. The foundations of the mathematical theory of elliptic variational inequalities were laid by Stampacchia [16], Hartman and Stampacchia [7], Lions and Stampacchia [11], and others. Evolutionary variational inequalities have been preliminary treated by Br�zis [2] who also connected the notion of variational inequality to convex subdifferential and maximal monotone operators. The theory of variational inequalities can be viewed as an important and significant extension of the variational principle of virtual work or power in inequality form, the origin of which can be traced back to Fermat, Euler, Bernoulli brothers, and Lagrange. The theory of variational inequalities and their applications represents the topics of several well-known classical monographs by Duvaut and Lions [4], Glowinski, Lions, and Tr�moli�res [6], Kinderlehrer and Stampacchia [10], Baiocchi and Capelo [1], Kikuchi and Oden [9], and so on. The notion of hemivariational inequality was first introduced by Panagiotopoulos [13] and is closely related to the development of the concept of the generalized gradient of a locally Lipschitz functional provided by Clarke [3]. Interest in hemivariational inequalities originated, similarly as in variational inequalities, in mechanical problems. From this point of view, the inequality problems in Mechanics can be divided into two main classes: that of variational inequalities, which is concerned with convex energy functions (potentials), and that of hemivariational inequalities, which is concerned with nonsmooth and nonconvex energy functions (superpotentials). Through the formulation of hemivariational inequalities, problems involving nonmonotone and multivalued constitutive laws and boundary conditions can be treated successfully mathematically and numerically. The theory of hemivariational inequalities and their applications was developed in several monographs by Panagiotopolous [13], Naniewicz and Panagiotopolous [12], and Haslinger, Mietten, and Panagiotopolous [8], among others. v