The paper by A. M. Perelomov generalizes the concept of coherent states, originally associated with the nilpotent group of Weyl, to arbitrary Lie groups. The introduction highlights the convenience of using coherent states in quantum theory, particularly in quantum optics and radiophysics, and questions whether similar systems exist for other Lie groups. The recent work by another author generalizes coherent states to some Lie groups but is limited to non-compact groups and does not preserve the invariance under group representation operators. Perelomov proposes a new method that can be applied to any Lie group and ensures the invariance under the group action. The paper constructs the system of coherent states and investigates its properties for the simplest Lie groups. The general properties of coherent states are discussed, including the definition and the role of the stationary subgroup \( H \) of a given state \( |\psi_0\rangle \). The coherent state \( |\psi_g\rangle \) is determined by the point \( x(g) \) in the factor space \( G/H \), and the paper also explores the one-dimensional unitary representation of \( H \) and the structure of its commutant \( H' \).The paper by A. M. Perelomov generalizes the concept of coherent states, originally associated with the nilpotent group of Weyl, to arbitrary Lie groups. The introduction highlights the convenience of using coherent states in quantum theory, particularly in quantum optics and radiophysics, and questions whether similar systems exist for other Lie groups. The recent work by another author generalizes coherent states to some Lie groups but is limited to non-compact groups and does not preserve the invariance under group representation operators. Perelomov proposes a new method that can be applied to any Lie group and ensures the invariance under the group action. The paper constructs the system of coherent states and investigates its properties for the simplest Lie groups. The general properties of coherent states are discussed, including the definition and the role of the stationary subgroup \( H \) of a given state \( |\psi_0\rangle \). The coherent state \( |\psi_g\rangle \) is determined by the point \( x(g) \) in the factor space \( G/H \), and the paper also explores the one-dimensional unitary representation of \( H \) and the structure of its commutant \( H' \).