Abdi Tadesse (PhD)Eshetu Assaye2018-07-112023-11-042018-07-112023-11-042014-08http://etd.aau.edu.et/handle/123456789/8079In this paper, we investigate some boundary value problems for two dimensional harmonic functions. That is basic introduce new tools for solving Dirichlet problems, Poisson’s equations and Neumann problems with Green’s function G( x; y; x0 y0) =1/2in( x –y0)2+( x – y0)2) + h (x ,y, x,0 y0) Where h is harmonic on the region and h(x, y, x0 , y0 ) =-1/2in ( x – x0)2 + y - y 0)2)on the boundary  . Roughly speaking Green’s function for a given region Ω and that can be used to solve any Dirichlet problems or Poisson problems on Ω. In the same way that the Poisson’s kernel on the real line can be used to solve Dirichlet problems in the upper half planeenGreens Functions and Boundary Value ProblemsThesis