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The Barrel Toroid Magnet is part of the Magnet System of the ATLAS Detector for the LHC. It provides the magnetic field required by the muon spectrometer. It consists of eight flat superconducting coils and will extend over a length of 26 meters with an inner bore of 9 meters and an outer diameter of 20 meters. The general design (pancakes, coil casing, tie rods, circular cryostats and warm voussoirs) has been presented in MT15. The present paper concentrates on the technological developments for the B0 model coil and for the BT coils: industrial production of conductor, welding technique for the coil casing, prestress of the coil with bladders, cold to warm supports, construction and assembly of the cryostat.