The discovery of superconductivity is over 100 years old. While superconducting materials have been studied in much detail over the past 100 years, it remains a grand intellectual challenge to understand how metals completely lose electric resistivity at low temperatures, and it remains an open question whether room temperature superconductivity can be achieved. Superconductivity based technologies are gradually being commercialized, in powerful magnetic field generators, SQUID magnetometers, Josephson junction amplifiers, microwave filters, and superconducting qubits. The development of these practical technologies would also benefit from an improved understanding of superconductor physics.The vast collection of superconductivity related measurement data, accumulated over the past 100 years, reveals quantitative formulas that characterize superconductivity. The most important such formulas are the London equation, the London moment formula, the Josephson frequency formula, the Uemura scaling, and the Roeser-Huber formula. A correct theory of superconductivity must rigorously derive all of these formulas - without involving ad-hoc assumptions or fitting parameters. While the currently favored theory of superconductivity assumes the existence of free-flowing electron pairs whose kinetic energy is near the Fermi energy level, the essential superconductivity phenomena are in fact incompatible with such free-flowing electron pairs.In this book, we develop the theory of electrons' Bose-Einstein condensation. The key is to correctly calculate both the microscopic interaction and the macroscopic thermodynamics of Bose-Einstein condensed electrons. Recognizing that only a fraction of electrons condenses at the transition point, a realistic calculation of Bose-Einstein condensation temperature requires evaluating the thermodynamic balance between coherent and incoherent electron populations. All results are derived through mathematically rigorous calculations that are explained step by step.After clarifying the dynamics of Bose-Einstein condensed electrons from first principles, the essential formulas of superconducting materials emerge naturally: this book contains rigorous derivations of the London equation, the London moment formula, the Josephson frequency formula, the Uemura scaling, and the Roeser-Huber formula. For most of these formulas, our book contains their first mathematically and physically correct derivation. We also review a large number of experiments that show direct signatures of Bose-Einstein condensation, including the well-known coherence of superconducting electrons.While Bose-Einstein condensed electron states generally arise in the conduction band, nothing in the theory is specific to just that electron population. This leads to the question: can ordinary electron orbitals host Bose-Einstein condensed electrons? We present experimental investigations of this question, with surprising answers.At the end of this short journey, the reader is rewarded by understanding how superconductivity really works, and learns about unexpected new materials comprising Bose-Einstein condensed electron orbitals.