The Advanced GAmma Tracking Array (AGATA) is a European project to develop and operate the next generation γ-ray spectrometer. AGATA is based on the technique of γ-ray energy tracking in electrically segmented high-purity germanium crystals. This technique requires the accurate determination of the energy, time and position of every interaction as a γ ray deposits its energy within the detector volume. Reconstruction of the full interaction path results in a detector with very high efficiency and excellent spectral response. The realisation of γ-ray tracking and AGATA is a result of many technical advances. These include the development of encapsulated highly segmented germanium detectors assembled in a triple cluster detector cryostat, an electronics system with fast digital sampling and a data acquisition system to process the data at a high rate. The full characterisation of the crystals was measured and compared with detector-response simulations. This enabled pulse-shape analysis algorithms, to extract energy, time and position, to be employed. In addition, tracking algorithms for event reconstruction were developed. The first phase of AGATA is now complete and operational in its first physics campaign. In the future AGATA will be moved between laboratories in Europe and operated in a series of campaigns to take advantage of the different beams and facilities available to maximise its science output. The paper reviews all the achievements made in the AGATA project including all the necessary infrastructure to operate and support the spectrometer.