The Enrico Fermi Schools, a cultural initiative promoted by the Italian Physical Society (SIF), were initiated in 1953 in a period that marked the beginnings of what is now called cosmic ray astrophysics. Indeed, the very first edition of the School focused on the contribution of cosmic ray physics to the laws of elementary particle physics. Almost seventy years later, another School has been focusing on the foundations of cosmic ray astrophysics, and this book contains the lectures presented as Course 208 of the prestigious International School of Physics Enrico Fermi, Foundations of Cosmic Ray Astrophysics, held in Varenna, Italy from 23 to 29 June 2022. Topics covered in the book range from particle acceleration to cosmic ray transport, and from radiation processes to feedback of cosmic rays in galaxy formation. In particular, a thorough description of the physics of cosmic ray transport in turbulent magnetic fields, and of the production of magnetic perturbations in the presence of cosmic ray gradients is provided, both these phenomena being essential in describing particle acceleration at shocks and the transport of cosmic rays within the galaxy. The transport of cosmic rays in different environments is also discussed. This area of research has received an extraordinary boost in recent times, thanks to the now unprecedented accuracy of observations, and to the possibility of testing new ideas and complex scenarios offered by recent developments in numerical simulation, and the book will be of interest to all those working in the field of high energy astrophysics.