QUBIC is an instrument aiming at measuring the B mode polarisation anisotropies at medium scales angular scales (30-200 multipoles). The search for the primordial CMB B-mode polarization signal is challenging, because of many difficulties: smallness of the expected signal, instrumental systematics that could possibly induce polarization leakage from the large E signal into B, brighter than anticipated polarized foregrounds (dust) reducing to zero the initial hope of finding sky regions clean enough to have a direct primordial B-modes observation. The QUBIC instrument is designed to address all aspects of this challenge with a novel kind of instrument, a Bolometric Interferometer, combining the background-limited sensitivity of Transition-Edge-Sensors and the control of systematics allowed by the observation of interference fringe patterns, while operating at two frequencies to disentangle polarized foregrounds from primordial B mode polarization. Its characteristics are described in details in this Technological Design Report.