This paper presents methods for analyzing anisotropic flow in relativistic nuclear collisions, focusing on the Fourier expansion of azimuthal distributions. The key idea is to use the Fourier coefficients to characterize different types of anisotropies, such as directed and elliptic flow, which correspond to the first and second harmonics, respectively. The event plane resolution is crucial for accurately determining these coefficients, as it accounts for the finite multiplicity of events. The event plane is determined from the anisotropic flow itself, and the resolution is estimated using correlations between sub-events. The Fourier expansion allows for the calculation of flow coefficients by dividing the observed coefficients by the event plane resolution. The resolution depends on the harmonic used to determine the event plane and the order of the calculated coefficient. The paper also discusses the importance of correcting for non-flow correlations, which can affect the results. Additionally, a method is described for introducing flow into a Monte Carlo event generator by modifying the azimuthal angles of particles. The analysis of anisotropic flow is important for understanding collective behavior in high-energy collisions and has implications for various measurements, including two-particle correlation analyses. The methods presented are applicable to a wide range of harmonic orders and provide a framework for studying the evolution of flow in nuclear collisions.This paper presents methods for analyzing anisotropic flow in relativistic nuclear collisions, focusing on the Fourier expansion of azimuthal distributions. The key idea is to use the Fourier coefficients to characterize different types of anisotropies, such as directed and elliptic flow, which correspond to the first and second harmonics, respectively. The event plane resolution is crucial for accurately determining these coefficients, as it accounts for the finite multiplicity of events. The event plane is determined from the anisotropic flow itself, and the resolution is estimated using correlations between sub-events. The Fourier expansion allows for the calculation of flow coefficients by dividing the observed coefficients by the event plane resolution. The resolution depends on the harmonic used to determine the event plane and the order of the calculated coefficient. The paper also discusses the importance of correcting for non-flow correlations, which can affect the results. Additionally, a method is described for introducing flow into a Monte Carlo event generator by modifying the azimuthal angles of particles. The analysis of anisotropic flow is important for understanding collective behavior in high-energy collisions and has implications for various measurements, including two-particle correlation analyses. The methods presented are applicable to a wide range of harmonic orders and provide a framework for studying the evolution of flow in nuclear collisions.