In this thesis the gamma distribution is considered for the reason of it's appearance in many statistical fields of applications. Some mathematical and statistical properties of the distribution are collected and unified. Moments and higher moments are illustrated and two methods of estimation for the distribution parameters are discussed theoretically and assessed practically. A new proposed method of approximation to the cumulative distribution function is derived and it showed practically a high performance in comparison with four well known methods of approximation. Finally five procedure for generating random variates from gamma distribution are discussed and their efficiencies are compared theoretically and practically by Monte-Carlo simulation.