Gedif, Tsegaye (PhD)Damtew, Takele2019-04-292023-11-092019-04-292023-11-092017-09-05http://etd.aau.edu.et/handle/123456789/18165This thesis provides an overview of harmonic functions of the following topic a) Some basic results like, Maximum principle, uniqueness Theorem and Green’s Formula. b) The fundamental properties of harmonic functions, Results like Poisson’s Integral Formula and its properties C) The basic theory regarding harmonic functions and positive harmonic functions. . Moreover, in this thesis we plan to focus on the advance theory of harmonic functions. Finally we give the detail prove of the Harnack’s Inequality and Harnack’s TheoremenOn Basic propertiesHarmonic FunctionsPositive HarmonicFunctionThesis