  This is the content of the lectures given by the author at the winter school
KAWA3 held at the University of Barcelona in 2012 from January 30 to
  February 3. The main goal was to give an account of viscosity techniques and
to apply them to degenerate Complex Monge-Amp\`ere equations following recent
works of P. Eyssidieux, V. Guedj and the author.
  We will survey the main techniques used in the viscosity approach and show
how to adapt them to degenerate complex Monge-Amp\`ere equations.
  The heart of the matter in this approach is the "Comparison Principle" which
allows us to prove uniqueness of solutions.
  We will prove a global viscosity comparison principle for degenerate complex
Monge-Amp\`ere equations on compact K\"ahler manifolds and show how to combine
Viscosity methods and Pluripotential methods to get "continuous versions" of
the Calabi-Yau and Aubin-Yau Theorems in some degenerate situations. In
particular we prove the existence of singular K\"ahler-Einstein metrics with
continuous potentials on compact normal K\"ahler varieties with mild
singularities and ample or trivial canonical divisor.
