In the present article a linear theory is developed for the absorption and conversion of electromagnetic waves in a planarly stratified, isotropic, warm plasma for arbitrary angles of incidence. In particular the case is investigated in which the frequency of the wave is equal to the local plasma frequency somewhere in the plasma (resonance plane). The polarization of the waves considered here is such that the electric field has a component parallel to the gradient of the plasma density (TM-polarization). The temperature is assumed to be constant. The given theory is more general than the existing theories for the following reasons: 1) The unperturbed electric field due to the inhomogeneity has been incorporated. 2) Better approximations away from the resonance plane are given. 3) The theory holds for arbitrary density profiles. Errors in the existing literature are corrected. The problem is studied by means of internal-boundary-layer-theory and Langer's method. Explicit expressions for the behaviour of the various field components and the pressure perturbation as well as the linear excitation of a plasma wave are given in the whole region of interest.