The numerical renormalization group (NRG) method, developed by Wilson in the early 1970s, is a powerful tool for studying quantum impurity systems. This review provides an introduction to the NRG method, including its application to various quantum impurity problems such as the Kondo effect, non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems like the spin-boson model, and lattice systems within the dynamical mean-field theory (DMFT). The NRG method involves a series of steps: logarithmic discretization of the bath spectral function, mapping the discretized model onto a semi-infinite chain, iterative diagonalization of the chain, and analysis of the many-particle spectra. The review covers the technical details of these steps and discusses the calculation of physical quantities, including thermodynamic and static properties, as well as dynamic quantities in equilibrium and non-equilibrium conditions. The NRG method has been successfully applied to a wide range of systems, from the standard Kondo effect to complex lattice models, and continues to be an important tool for advancing our understanding of quantum impurity systems.The numerical renormalization group (NRG) method, developed by Wilson in the early 1970s, is a powerful tool for studying quantum impurity systems. This review provides an introduction to the NRG method, including its application to various quantum impurity problems such as the Kondo effect, non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems like the spin-boson model, and lattice systems within the dynamical mean-field theory (DMFT). The NRG method involves a series of steps: logarithmic discretization of the bath spectral function, mapping the discretized model onto a semi-infinite chain, iterative diagonalization of the chain, and analysis of the many-particle spectra. The review covers the technical details of these steps and discusses the calculation of physical quantities, including thermodynamic and static properties, as well as dynamic quantities in equilibrium and non-equilibrium conditions. The NRG method has been successfully applied to a wide range of systems, from the standard Kondo effect to complex lattice models, and continues to be an important tool for advancing our understanding of quantum impurity systems.