We present some results from our HST archival image study of 71 QSO host galaxies. The objects are selected to have z less than or equal to 0.46 and total absolute magnitude M(sub v) less than or equal to -23 in our adopted cosmology (H(sub 0) = 50 kilometers per second Mpc(sup-1), q(sub 0) = 0.5, lambda = 0)). The aim of this initial study is to investigate the composition of the sample with respect to host morphology and radio loudness, as well as derive the QSO host galaxy luminosity function. We have analyzed available WFPC2 images in R or I band (U in one case), using a uniform set of procedures. The host galaxies span a narrow range of luminosities and are exceptionally bright, much more so than normal galaxies, usually L greater than L*(sub v). The QSOs are almost equally divided among three subclasses: radio-loud QSOs with elliptical hosts, radio-quiet QSOs with elliptical hosts, and radio-quiet QSOs with spiral hosts. Radio-loud QSOs with spiral hosts are extremely rare. Using a weighting procedure, we derive the combined luminosity function of QSO host galaxies. We find that the luminosity function of QSO hosts differs in shape from that of normal galaxies but that they coincide at the highest luminosities. The ratio of the number of quasar hosts to the number of normal galaxies at a luminosity L*(sub v) is R = (Lv/11.48L*(sub v))(sup 2.46), where L*(sub v) corresponds to M*(sub v)= -22.35, and a QSO is defined to be an object with total nuclear plus host light M(sub v) less than or equal to -23. This ratio can be interpreted as the probability that a galaxy with luminosity L(sub V) will host a QSO at redshift z approximately equal to 0.26.