Photoelectron spectroscopy is the study of the kinetic energies of the photoelectrons ejected from gaseous species by monochromatic radiation. Subtraction of these kinetic energies from the incident photon energy yields the binding energies of the orbitals from which the electrons were removed. The work to be described falls into two main parts. The first is concerned with the development of a new type of spectrometer to measure such kinetic energies. To date, all photoelectron spectrometers designed specifically for gaseous samples have employed a retarding field of cylindrical geometry to energy-analyze the emitted photoelectrons. Consideration of the angular distribution with which electrons are ejected during the photoionization process indicates that a spectrometer utilizing a retarding field of spherical geometry should give a stopping curve, the first differential of which is close to the true photoelectron kinetic energy spectrum. Instruments of both cylindrical and spherical geometry were constructed and their properties tested. Conclusive evidence for the superiority of the spherical system is presented together with details of its construction and operation. The second part of this thesis/contains the results of photoelectron spectroscopic studies on twenty-one atoms and molecules (Ar, Kr, Xe, H₂, HD, D₂, N₂, CO, O₂, NO, HF, HCl , HBr, HI, F₂, Cl₂, Br₂, I₂,N₂O, NO₂ and NH₃). The energies of the ionic states could be obtained to a precision of 0.01 ev., and they agree, well with available spectroscopic data. In many instances new ionic states are found, and where possible they are correlated with states predicted by molecular orbital theory. Relative transition probabilities to the various ionic states are also obtained by this method. They are, in nearly every case, the only experimental values available. The spacings and relative probabilities for formation of ionic vibrational levels have been measured for certain states in H₂, HD, D₂, N₂, CO, O₂, NO, F₂, N₂O and NO₂ and the values obtained compared with spectroscopic and calculated data where this is available. / Science, Faculty of / Chemistry, Department of / Graduate