The course is divided into two parts: theory of machining plus tools, and theory of metal forming plus tools. In the first part, students gain the basic knowledge in the area of taking chips, machining methods and experimentally established relations in the theory of machining. The principles of designing cutting tools are discussed, as well as the optimization of the cutting process, the choice of cutting materials and their effect on the durability and service life of tools. In the second part the students acquire the basic knowledge of and skills in mathematically describing metal-forming processes while applying the physical, chemical, mechanical and thermodynamic principles of the transition of metallic bodies from elastic into plastic state in the course of their plastic deformation into the required shape. Within this subject the loading of the metal-forming tools is dealt with and provisions are made for a first design of the forming machine.