The use of topology optimization and methods of optimization in general in engineering has great untapped potential. Optimization methods represent an excellent tool not only for saving time and resources but also for obtaining efficient and interesting structures. The first part of this work presents certain fundamental topics about optimization in mechanical engineering. Different types of optimization have been explained and certain most important methods of topology optimization have been described in detail. In two separate chapters the applications of topology optimization in product design and in additive manufacturing are also presented. In the main part of the work, a topology optimization of a geometry was performed in ANSYS 19.1 software. The whole process of optimization is presented and the work in the software is explained. Also explained is the application of ANSYS manufacturing constraints for the purpose of modifying the optimized geometry for additive manufacturing. The result of the topology optimization was a geometry, which in comparison with the original geometry weighed 51% less. A numerical analysis of the original and optimized geometries was also performed which showed an increase of 7,8 percent in maximum stress, a shift of the location of maximum stress and a considerable increase of deformation by 36,2 percent. After the analyses have been performed the optimized and original geometries were successfully manufactured on a Prusa i3 3d printer. Attached is a report of optimization that contains all the settings required for optimization.