Stochastic Differential Equations, Backward SDEs, Partial Differential EquationsThis research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients.