ATLAS measurements of the azimuthal anisotropy in lead-lead collisions at root(NN)-N-S = 2.76 TeV are shown using a dataset of approximately 7 mu b(-1) collected at the LHC in 2010. The measurements are performed for charged particles with transverse momenta 0.5 < p(T) < 20 GeV and in the pseudorapidity range vertical bar eta vertical bar < 2.5. The anisotropy is characterized by the Fourier coefficients, vn, of the charged-particle azimuthal angle distribution for n = 2-4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the v(n) coefficients are presented. The elliptic flow, v(2), is obtained from the two-, four-, six-and eight-particle cumulants while higher-order coefficients, v(3) and v(4), are determined with two-and four-particle cumulants. Flow harmonics v(n) measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to v(n) measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multiparticle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.