The Double Chooz neutrino oscillation experiment will perform a highly sensitive measurement of the neutrino mixing angle θ13. The Double Chooz project will utilize two detectors, a near one providing the unoscillated neutrino flux coming from the two reactor cores of the Chooz nuclear plant (France), and a far detector measuring the neutrino flux after oscillation. The signal comparison between the two detectors will allow to push down the θ13 limit at very low values. Double CHOOZ far detector under construction will start taking data beginning of next year and in about 1.5 years will be able to set the limit sin2(2θ13)<0.06, the present limit being sin2(2θ13)<0.2. At that moment, the near detector will also be ready and help to set this limit at sin2(2θ13)<0.03 in less than 3 years. The mixing angle θ13 is the last non-measured oscillation parameter of the neutrino mixing matrix. The possibility of measuring the sin2(2θ13) or lowering the existing limit to a few percent would also allow selection of the best means to search for the CP-phase in the lepton sector. In this presentation a detailed description of the Double Chooz experiment will be done.