ATLAS measurements of the azimuthal anisotropy in lead–lead collisions at $$\sqrt{s_{\mathrm {NN}}}=2.76$$ TeV are shown using a dataset of approximately 7 $$\upmu $$ b $$^{-1}$$ collected at the LHC in 2010. The measurements are performed for charged particles with transverse momenta $$0.5<p_{\mathrm {T}}<20$$ GeV and in the pseudorapidity range $$|\eta |<2.5$$ . The anisotropy is characterized by the Fourier coefficients, $$\mathrm {v}_n$$ , 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 $$\mathrm {v}_n$$ coefficients are presented. The elliptic flow, $$\mathrm {v}_2$$ , is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, $$\mathrm {v}_3$$ and $$\mathrm {v}_4$$ , are determined with two- and four-particle cumulants. Flow harmonics $$\mathrm {v}_n$$ measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to $$\mathrm {v}_n$$ measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multi-particle 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.