Abstarct: Geometric programming is a relatively new method for solving a class of nonlinear programming problems. In this thesis, we examine geometric programming problems and their solution methods. First, we present a definition of the basic geometric programming problem and posynomials. Then, we obtain the solution of an unconstrained geometric programming problem using two methods: differential calculus and arithmetic-geometric mean inequalities. We also state the primal-dual relationships for this problem and investigate sufficient optimality conditions. In the constrained case, we present the primal-dual relationships and solve problems with zero and one degrees of difficulty. In addition to the above, we investigate the complementary programming problem and show that this problem transforms into a geometric programming problem in special cases. Various extensions of geometric programming, including problems with monomial objective functions, signomials, geometric-linear combinations, and log-monomials, are also discussed, and it is examined under what conditions they convert to geometric programming. Several examples of applications of geometric programming are also presented in this thesis.