The book deals with the mathematical theory of vector variational ineq ualities with special reference to equilibrium problems. Such models h ave been introduced recently to study new problems from mechanics, str uctural engineering, networks, and industrial management, and to revis it old ones. The common feature of these problems is that given by the presence of concurrent objectives and by the difficulty of identifyin g a global functional (like energy) to be extremized. The vector varia tional inequalities have the advantage of both the variational ones an d vector optimization which are found as special cases. Among several applications, the equilibrium flows on a network receive special atten tion.