Computing the volume and integral points of a polytope 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 volumeof a convex polytope are recalled. Chapter two, present some methods for computing the coefficients of Ehrhart polynomial that depend on the concepts of residue theorem in complex analysis. Chapter three, a method for finding the volume of a cyclic polytope is presented and some basic concepts and remarks about the...