The book "Basics of Aerothermodynamics" provides a comprehensive introduction to the fundamentals of aerothermodynamics, particularly concerning winged reentry vehicles and air-breathing hypersonic flight and acceleration vehicles. In this revised second edition, most of the classical topics remain unchanged, while access to specific practical subjects has been improved. The book covers central aspects such as the transport of momentum, energy, and mass, as well as the effects of real gases and the phenomena of inviscid and viscous flow. The recent successes of the X-43A and X-51A demonstrate the relevance of the topics discussed, especially the viscous effects and the aerothermodynamics of radiation-cooled vehicle surfaces. A new chapter is dedicated to examples of viscous thermal surface effects, highlighting the complexity of these phenomena that are significant for air-breathing hypersonic aircraft.