The non-LTE equation of transfer in the presence of a magnetic field is presented. The theory is valid for arbitrary Zeeman patterns and the field is inhomogeneous. The Faraday effect is taken into account. The LTE source function (Planck function) is substituted by four functions, which generally depend on the direction and population of the levels. The vector source function ( is the result of a detailed consideration of the emission processes in the presence of a magnetic field. These processes are studied by two different methods and the results are shown to be equivalent. The induced emission is neglected. If the Zeeman levels are unpolarized and the Boltzmann law for populations is valid, the non-LTE equation of transfer will change into the well-known LTE theory. The density matrix formulation is widely used. Radiative transition rates of two Zeeman levels of the atom in a general field of radiation (whose Stokes parameters are a function of direction) are calculated. These rates enter into the equation of statistical equilibrium which, together with the equation of transfer, form the complete set of equations for the Stokes parameters and populations of the Zeeman levels.