The main topic of the book are the superconducting dipole and quadrupole magnets needed in high-energy accelerators and storage rings for protons, antiprotons or heavy ions. The basic principles of low-temperature superconductivity are outlined with special emphasis on the effects which are relevant for accelerator magnets. Properties and fabrication methods of practical superconductors are described. Analytical methods for field calculation and multipole expansion are presented for coils without and with iron yoke. The effect of yoke saturation and geometric distortions on field quality is studied. Persistent magnetization currents in the superconductor and eddy currents the copper part of the cable are analyzed in detail and their influence on field quality and magnet performance is investigated. Superconductor stability, quench origins and propagation and magnet protection are addressed. Some important concepts of accelerator physics are introduced which are needed to appreciate the demanding requirements on field quality in large storage rings. The operational experience with the superconducting HERA collider serves as an illustration. Finally superconducting correction coils and practical construction and fabrication methods of accelerator magnets are discussed. The physical and technical principles described in the book are substantiated with a wealth of experimental data on multipoles, persistent- and eddy-current effects, quench performance and much more.