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An international collaboration at DESY is currently studying the possibilities of a new type of particle accelerator: the superconducting linear collider. Developed under the project name TESLA, which stands for TeV Energy Superconducting Linear Accelerator, the facility would be placed in a 33-km long tunnel and would work at the energy range of 0.5 to 0.8 TeV. This paper is about one of the components of the accelerator: the superconducting magnets. A total of 801 magnet packages would be necessary for the accelerator: 370 long quadrupoles with a dipole, 370 long quadrupoles with two dipoles, 30 short quadrupole doublets with one dipole, and 31 short quadrupole doublets with two dipoles. The working temperature is 2 K, using superfluid helium as coolant. Magnetic and mechanical calculations are performed to evaluate the most adequate solution. Quench propagation is also simulated by means of numerical methods. Some guidelines for the fabrication of the industrial series are developed later on.