The measurement of the azimuthal anisotropy of charged particles produced in lead–lead collisions at SNN=2.76TeV is reported. The Fourier coefficients vn of the azimuthal angle distribution are obtained using multi-particle cumulants. The results on the transverse momentum and centrality dependence of the elliptic flow (v2) obtained from two-, four-, six- and eight-particle cumulants are presented. Higher-order harmonics, v3 and v4, are also derived using two- and four-particle cumulants and shown as a function of centrality and transverse momentum. A reduction of contributions from correlations not related to the collective flow are discussed. Event-by-event fluctuations of the flow harmonics are also presented as a function of transverse momentum and the collision centrality.