Abstarct: There are three types of optimization methods in literature called mathematical, optimality criteria and mexta-heuristic baxsed approaches. In this thesis, the level set method which is from mathematical baxsed approaches is applied for topology optimization of structures. In order to describe the boundaries of a structure, zero level of an implicit function from a higher dimension with respect to the geometry, called level set function, is considered. Changes in this function can easily model splitting and merging of the structural elements. Strain energy minimization subject to volume constraint, volume minimization subject to local stress limitations constraints and multi objective function “strain energy and volume” minimization subject to local stress limitations constraints are three types of optimization problems that discussed in this thesis. Since derivatives of objective and constraints functions are needed in LSM, sensitivity analysis forms part of this research and an analytical approach is developed for this purpose. Also, In order to satisfy the volume constraint a simple method is introduced baxsed on sensitivity analysis. For the sake of comparison and verification the results are compared with conventional level set method by demonstrating a few examples. The IsoGeometric Analysis (IGA) method is employed for structural analysis. In this method unknown function (deformation) is approximated by Non-Uniform Rational B-Splines (NURBS) basis functions which are also used for creating geometry of the structure and construct the level set function. Consequently, by changing the position of control points of NURBS, the geometry and the analysis model will change, simultaneously. Therefore, there is no need to regenerate the analysis model during the optimization iterations, which is the case when the Finite Element (FE) method is used as the analysis engine. In order to verify the derived sensitivity equations, demonstrate the ability of LSM in solving topology optimization problems and check the code that written in this thesis, several two dimensional illustrative examples are presented.