Fluctuations and correlations of flow in heavy-ion collisions measured by ALICE

<!--HTML-->Heavy-ion collisions at ultra-relativistic energies at the LHC provide a unique opportunity to study the strongly interacting quark-gluon plasma (QGP). Anisotropic flow phenomena provide valuable information on the initial conditions of heavy-ion collisions, the transport coefficients, and the dynamic evolution of the created QGP. In this talk, we present investigations of the transverse-momentum dependent flow vector fluctuations in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. Using newly proposed multiparticle correlations, for the first time we separate the potential contributions from flow angle and flow magnitude fluctuations and report the first evidence of both effects in Pb–Pb collisions. In addition, we discuss how to use event shape engineering (ESE) techniques to select the initial conditions and change the event-by-event $v_n$ distribution. Furthermore, we show a novel approach to study the correlations between different order coefficients $v_n$ and $v_m$, as well as the nonlinear flow modes, using the ESE technique. Together with the comparisons to the state-of-the-art hydrodynamic calculations, we can significantly improve the understanding of the initial conditions and the dynamic evolution of the created systems in heavy-ion collisions at the LHC.