Some basic references :

• M.Bardi and I. Capuzzo Dolcetta : Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston,1997

• G. Barles : Solutions de viscosité des équations de Hamilton-Jacobi. Collection ``Mathématiques et Applications'' de la SMAI, no 17, Springer-Verlag (1994).

• M.G Crandall, H.Ishii and P.L Lions : User's guide to viscosity solutions of second order Partial differential equations. Bull. Amer. Soc. 27 (1992), pp 1-67.

• W.H Fleming and H.M Soner : Controlled Markov Processes and Viscosity Solutions. Applications of Mathematics, Springer-Verlag, New-York, 1993.

• P.L. Lions : Generalized Solutions of Hamilton-Jacobi Equations. Pitman, Boston, 1982.

• Viscosity solutions and applications : Lectures given at the 2nd C.I.M.E. Session held in Montecatini Terme, June 12--20, 1995. Edited by I. Capuzzo Dolcetta and P. L. Lions. Lecture Notes in Mathematics, 1660. Fondazione C.I.M.E..

A course in french :

• Post-dea course of G. Barles on viscosity solutions (organised by J.M. Roquejoffre in 1997 at the University Paul Sabatier (Toulouse)-in french) (pdf)