Viscosity Solutions and Applications : Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme Italy June 12–20 1995 The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations and some of its most relevant applications to optimal control theory for deterministic and stochastic systems front propagation geometric motions and mathematical finance. The volume forms a state of the art reference on the subject of viscosity solutions and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDEs systems theory stochastic processes