In the first part of the lecture, the use of turbocompressors (TC) in the process and chemical industry, in Carnot batteries for energy storage, in fuel cell systems, for hydrogen transportation in pipelines, and in consumer products are explained. The turbocompressors are classified according to their field of application, the fluid used and their operating range. Based on characteristic values, compressors of different designs are selected. This is followed by detailed considerations on the project planning, calculation and design of single- and multi-stage compressor systems, considering the thermodynamic principles and the particular mechanical design problems. Furthermore, the determination of characteristic curves, the operating behaviour and the control of compressors in single- and multi-stage compressor systems are considered.