[en] The OPERA experiment at the Gran Sasso underground laboratory is searching for ν_μ → ν_τ oscillations in appearance mode in the CNGS neutrino beam. Four ν_τ candidate events have been found so far, using a sub-sample of data from the 2008-2012 runs. Given the number of analysed events and the low background, ν_μ → ν_τ oscillations are established with a significance of 4.2 σ. In this paper the data analysis is discussed, with emphasis on the background constraints obtained using dedicated data-driven control samples. We present also the analysis of the τ neutrino and electron neutrino data in the framework of the 3+1 sterile neutrino model. The measurement of the muon charge ratio in the collected cosmic ray sample is also reported. (paper)