This book outlines a path that, in addition to providing the necessary foundation for dealing with the study of AC systems, allows an overview and an introduction to some of the powerful mathematical ideas and methods, fundamental to many areas of current science and technology. Besides a theoretical review for the practitioner, it can be profitably used as a bridge in the transition from high-school mathematics to specialized university courses. This is why the reader is accompanied on the journey by "mathematical interludes," in which he/she will find useful reminders and insights. It also constitutes a cultural proposal dedicated to all those who, like I. Newton, holding between two fingers the grain of their knowledge, always see, in the background, the ocean of the unknown.- 1 - SINUSOIDAL ELECTRICAL QUANTITIES- 2 - SINUSOIDS, PHASORS AND COMPLEX NUMBERS- 3 - IMPEDANCE AND REACTANCE- 4 - ADMITTANCE AND AC NETWORKS- 5 - RESONANCE- 6 - ELECTRICAL POWER IN AC SYSTEMS- 7 - TRANSIENTS AND OSCILLATIONS- 8 - THE FOURIER SERIES- 9 - VECTOR AND HILBERT SPACES-10 - THE FOURIER TRANSFORM - SANDRO RONCA - After studying Physics at the University of Padua, he dedicated himself to teaching Electrical Technologies and Computer Science in Upper Secondary Education Technical Schools, deepening the didactic aspects. He has studied computer networks in depth and designed, at the request of Industrial Associations, courses for System Analysts and IT Security Managers.