Abstarct: Topology optimization is one of the most important types of structural optimization problems that seeks optimal distribution of materials in the design domain. To achieve this, it is important to select the appropriate objective function and constraint. In this thesis, topology optimization with the aim of weight minimization and considering fatigue constraint has been investigated. Since the isogeometric analysis in comparison with finite element method, has found a special place among researchers in this field and it has been able to act more accurately in geometry modeling and displacement calculation compared to previous methods, it has been used as one of the tools in this research. In isogeometric analysis, instead of using polynomial basis functions in finite elements, Non-Uniform Rational B-Splines basis functions are used to express geometry and approximation of displacement. For fatigue analysis the equivalent static analysis method has been used. To control fatigue failure, the modified Goodman fatigue failure criterion has been used and the computational time has been reduced by using the stress constraint clustering method. Due to the ubiquity and popularity of the level set method and the simplicity and high accuracy as well as its compatibility with the isogeometric analysis, this method has been used for topology optimization. In the level set method, the structural boundaries that are optimized are a model of dynamic boundaries that are introduced by an implicit function from a higher dimension, and the structural boundary by a definite level is introduced and a new boundary is obtained by solving the Hamilton-Jacobi equation. In order to verify the derived sensitivity equations, demonstrate the ability of LSM in solving topology optimization problems and check the code, written in this thesis, several two dimensional illustrative examples are presented.