This article deals with nonlinear semigroups of holomorphic mappings in a certain domain \(D\) in a complex Banach space \(X\). The authors prove the existence of the infinitesimal generator for such a semigroup and that this generator is a holomorphic mapping from \(D\) into \(X\), present some natural exponential formulas connecting a semigroup and its generator, describe conditions under which a given operator \(f\) is the generator of a semigroup of holomorphic mappings, investigate relations between properties of a semigroup of holomorphic mappings and the corresponding Cauchy problem, construct holomorphic retractions onto the stationary point sets of such semigroups.