We present a theoretical study of HF wave propagation through the ionosphere. The purpose is to illustrate how various propagation effects arise, firstly due to the large-scale structure of an ionospheric layer, secondly due to density perturbations present in that layer. Some results are well-known, others are new. The treatment is based on a report by Zernov and Lundborg (see IRF Scientific Report 215, 1993). The given model permits a fully analytic representation of the background electromagnetic field in the geometrical-optics approximation, but still gives a realistic description of propagation through an ionospheric layer. Since the model is continuous in all its derivatives, it has significant computational advantages. We illustrate the background field in terms of the rays, the eikonal and the level. The article also includes the skip distance fading. Using that field, we then investigate some effects of particular deterministic perturbations ɛ, viz. a wave-like and a local anisotropic Gaussian disturbance. We treat these cases in the geometrical-optics approximation and within single-scattering theory.