Our transition towards a cleaner and more sustainable future has seen an increase in the use of electrical energy in the functioning of our society. This implies the need to develop tools and methods which allow us to study electromagnetic devices and ensure their functioning for as long as possible. This requires us to use these tools to understand their behavior, not just as one component, but also in the entire systems in which they can be found, throughout their life cycle. This book provides electrical engineering students and researchers with the resources to analyze how synchronous machines behave over their entire field of operation, particularly focusing on hybrid excited synchronous machines (HESMs). The field of HESMs, although not a fundamental problem in the strict sense of the term, provides answers to a range of fundamental problems: the flux weakening of permanent magnet machines, energy optimization, and lastly the increasing costs of rare-earths permanent magnets.