"The course treats basic theory of stochastic differential equations and its relation with partial differential equation. This course includes the following topics Ito integrals – construction of the Ito integral – Some properties of the Ito integral – Extension of the Ito integral - Ito formula – Martingale representation theorem - Stochastic differential equations – Examples and some solution methods - The existence and uniqueness of solutions – Weak and strong solutions - Linear Stochastic differential equations - The generator of an Ito diffusion – The Dynkin formula – The Kolmogorov’s Backward equation – The Feynman – Kac formula – The Characteristic Operator – The Martingale problem -The Girsanov theorem. Applications to boundary value problems “The Combined Dirichlet – Poisson problem, The Dirichlet problem, The Poisson problem."