Introduction to viscosity solutions theory Can you recommend an introduction to viscosity solutions theory? More specifically, I'm looking for a modern treatment similar to Chapter 10 of Evans's Partial Differential Equations, but somewhat more detailed and comprehensive. 
(Of course, I'm aware of the User's Guide, but it is not quite what I'm looking for).

I would recommend the book by Bardi and Capuzzo-Dolcetta.
"Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations" Bardi, Martino, Capuzzo-Dolcetta, Italo
For something shorter and more introductory you can check out my notes:
http://math.umn.edu/~jwcalder/222BS16/viscosity_solutions.pdf
