RATRAN is a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. The approach is based on the Monte Carlo method, and incorporates elements from Accelerated Lambda Iteration. It combines the flexibility of the former with the speed and accuracy of the latter. Convergence problems known to plague Monte Carlo methods at large optical depth (>100) are avoided by separating local contributions to the radiation field from the overall transfer problem. The random nature of the Monte Carlo method serves to verify the independence of the solution to the angular, spatial, and frequency sampling of the radiation field. This allows the method to be used in a wide variety of astrophysical problems without specific adaptations. Moreover, the code can be applied to all atoms or molecules for which collisional rate coefficients are available and any axially symmetric source model. Continuum emission and absorption by dust is explicitly taken into account but scattering is neglected. We expect this program to be an important tool in analyzing data from present and future infrared and (sub-)millimeter telescopes.