This thesis provides an overview of harmonic functions of the following topicrna) Some basic results like, Maximum principle, uniqueness Theorem andrnGreen’s Formula.rnb) The fundamental properties of harmonic functions, Results like Poisson’srnIntegral Formula and its propertiesrnC) The basic theory regarding harmonic functions and positive harmonicrnfunctions. .rnMoreover, in this thesis we plan to focus on the advance theory of harmonic functions.rnFinally we give the detail prove of the Harnack’s Inequality and Harnack’s Theorem