This book explores spatial harmonic analysis (SHA) for characterizing and analyzing external magnetic fields in technical systems. Its strong emphasis on addressing real engineering challenges and a practical focus on both spherical and spheroidal harmonics set it apart, with the latter being valuable for analyzing objects with high aspect ratios. The content is particularly applicable to naval and spacecraft applications, as well as the rapidly growing field of autonomous unmanned vehicles, including aerial, surface, and underwater vehicles. In these contexts, precise control of magnetic signatures is crucial for navigation, detection avoidance, and overall operational effectiveness. The author presents multiple original concepts, including fast algorithms for spheroidal harmonic functions, which make them computationally feasible for real-world applications. Additionally, the use of magnetic energy as a general metric for the magnetic intensity of a given device is explored, as well as isodynamic surfaces to identify regions of maximum magnetic field extension.  Magnetic Signatures: Advanced Analysis for Modern Systems combines rigorous mathematical foundations with practical implementation strategies, making it an essential resource for designing and operating magnetically sensitive systems across various domains.