The electron theory of metals describes how electrons are responsible for the bonding of metals and subsequent physical, chemical and transport properties. This textbook gives a complete account of electron theory in both periodic and non-periodic metallic systems. The author presents an accessible approach to the theory of electrons, comparing it with experimental results as much as possible. The book starts with the basics of one-electron band theory and progresses to cover topics such as high Tc superconductors and quasicrystals. The relationship between theory and potential applications is also emphasized. The material presented assumes some knowledge of elementary quantum mechanics as well as the principles of classical mechanics and electromagnetism. This textbook will be of interest to advanced undergraduates and graduate students in physics, chemistry, materials science and electrical engineering. The book contains numerous exercises and an extensive list of references and numerical data.