The College of Science in the Department of Mathematics discussed a master thesis titled (Explicit Forms for Harnack's Inequality for Dirichlet Problem with some Applications of Poisson's Integral Formula and a Study for the Maximum Principle of Harmonic Functions) for postgraduate student Sarah Y.A. . The thesis aims to study Poisson's integral formula, giving an explicit form for Harnack's inequality in the open ball B,(0), and a study for the maximum principle of harmonic functions.