ATLAS measurements of the azimuthal anisotropy in lead–lead collisions at (Formula presented.) are shown using a dataset of approximately 7 (Formula presented.) collected at the LHC in 2010. The measurements are performed for charged particles with transverse momenta (Formula presented.) and in the pseudorapidity range (Formula presented.) The anisotropy is characterized by the Fourier coefficients, (Formula presented.), of the charged-particle azimuthal angle distribution for (Formula presented.). 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 (Formula presented.) coefficients are presented. The elliptic flow, (Formula presented.), is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, (Formula presented.), are determined with two- and four-particle cumulants. Flow harmonics (Formula presented.) measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to (Formula presented.) 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.