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
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