This study consists of four chapters. In the first chapter we have given some historical background of the problem, basic definitions and properties. Inhomogeneous
Cauchy-Riemann systems have been presented in Chapter 2. The operator T_Omega and the general solution of the inhomogeneous Cauchy-Riemann system have
also been discussed. Chapter 3 is devoted to the investigation of the theory of boundary value problems, in particular, Dirichlet problem for holomorphic functions in
Hölder spaces. In the last chapter we have considered the boundary value problems for the generalized analytic functions. Firstly, we have given the basic properties
of generalized analytic functions. Then the solution of the Dirichlet problem for a first order partial complex differential equation is given. Afterwards, the solution of a
Dirichlet problem for a second order partial complex differential equation is obtained, by reducing it into a system of first order partial complex differential equations.
Lastly we have derived some estimates for the solutions of the problem.

Keywords : Generalized analytic functions, holomorphic, Dirichlet problem, partial complex derivatives, complex integral operators.