Computing the volume and integral points of a polyhedron in Rn is a very important subject in different areas of mathematics. Chapter one give a short introduction, provide a sketch of what polytope looks like and how they behave with many examples. Some methods for finding the number of integral points inside a convex polytope are recalled. Chapter two, present some methods for computing the coefficients of Ehrhart polynomial that depend on the concepts of Dedekind sum and residue theorem in complex analysis. We give a method for computing the coefficients of the Ehrhart polynomial, cd-3,...