This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations.Brain Computations and Principles; and AI is about how the brain works, and about how brain computations compare to AI computations. In order to understand this, it is essential to know what is computed by different brain systems; how the computations are performed; and how the brain systems are connected. The aims of this book are to elucidate what is computed in many different brain systems; to describe current biologically plausible computational approaches and models of how each of these brain systems computes; to elucidate the principles of brain computations; to compare brain computations with those performed by AI systems; and to consider how understanding differences between brain computations and AI computations will benefit both.Understanding the brain in this way has enormous potential for understanding ourselves better in health and in disease. Potential applications of this understanding are to the treatment of the brain in disease; and to artificial intelligence which will benefit from knowledge of how the brain performs many of its extraordinarily impressive functions. This book is pioneering in taking this approach to brain function: to consider what is computed by many of our brain systems; how it is computed; what the connectivity is between different brain regions; the principles of operation of the brain; and comparing these to AI systems. This book thus considerably updates and extends Rolls' 2023 book Brain Computations and Connectivity.Brain Computations and Principles; and AI will be of interest to all scientists interested in brain function and how the brain works, whether they are from neuroscience, or from medical sciences including neurology and psychiatry, or from the area of computational science including machine learning and artificial intelligence, or from areas such as theoretical physics.