Optical systems in high precision equipment become increasingly more complex due to the raising number of optical mounts used for mounting and positioning of optical components. Additional, the installation of electronics and inert gas purging systems to protect the optics against the abrasive optical beam extends the amount of components in the optical system, while keeping the surface area of the overall optical system as small as possible. Recent developments in optical systems lead to innovations of optical flexure mounts towards a more compact, accessible and user-specific system with integrated functionality at consistently high standards of optical stability. Additive manufacturing, commonly named 3D printing, offers new possibilities of designing optical flexure mounts, since the layer-wise manufacturing approach allows the production of highly complex parts compared to traditional processes. Topology optimization is a mathematical design tool that can help to design these increasingly complex parts, such as the optical mount, by computing optimal material distributions for a given objective with a determined set of constraints and boundary conditions. The thesis objective is bilateral: The first research objective investigates the design of compliant mechanisms for industrial optical mounts by means of additive manufacturing. The second research objective investigates the suitability of Topology Optimization for designing compliant mechanisms for optical mounts. This research is providing insights into the working principles of optical mounts and compliant mechanisms as well as topology optimization and additive manufacturing. The present case studies demonstrate and evaluate topology optimization design techniques for compliant structures and mechanisms. Further, the use of additive manufacturing for compliant optical mounts mechanisms designs is evaluated.