Particle accelerators are a major invention of the 20th century. In the last eight decades, they have evolved enormously and have fundamentally changed the way we live, think and work. Accelerators are the most powerful microscopes for viewing the tiniest inner structure of cells, genes, molecules, atoms and their constituents such as protons, neutrons, electrons, neutrinos and quarks. This opens up a whole new world for materials science, chemistry and molecular biology.Accelerators with megawatt beam power may ultimately solve a critical problem faced by our society, namely, the treatment of nuclear waste and the supply of an alternative type of energy. There are also tens of thousands of small accelerators all over the world. They are used every day for medical imaging, cancer therapy, radioisotope production, high-density chip-making, mass spectrometry, cargo x-ray/gamma-ray imaging, detection of explosives and illicit drugs, and weapons. This volume provides a comprehensive review of this driving and fascinating field.