Extensive measurements of slow-neutron inelastic scattering from liquid argon at 84.5°K have been made using cold and thermal neutrons. The cold-neutron experiments were performed using a rotating-crystal spectrometer. A triple-axis spectrometer in its "constant-Q" mode of operation was used for the thermal-neutron measurements. A wave-vector transfer (Q) range of 0.4 to 6.0 Å-1 was covered, a range which extends through the third peak in the diffraction pattern of liquid argon. Some data were also collected at 87.9°, 90.0° and 92.3°K. The measurements at 84.5°K were converted to Van Hove's S(Q, ω) which was in turn converted to the intermediate scattering function, I(Q, t), and then to Van Hove's space-time self- and pair-correlation functions. I(Q, t) was determined for Q<=6 Å-1 and t<=6×10-12 sec. The self-correlation function, Gs(r, t), has been completely mapped in the time range 0-2×10-12 sec and is found to be Gaussian in shape to within our experimental accuracy (about 10 to 15%). The width of Gs(r, t) follows the law obtained by assuming Fick's law for diffusion to hold. This suggests that in argon diffusion is a simple process, unlike that in other liquids investigated by means of neutrons. This conclusion is also supported by measurements on the temperature dependence of the energy width. These measurements give an activation energy of roughly 700 cal/mole for diffusion, in fair agreement with previous measurements on the temperature dependence of the diffusion constant. The time-dependent pair-correlation function has also been determined in the time range of 0-2×10-12 sec. From 2×10-12 to 6×10-12 sec, a weighted combination of Gs(r, t) and Gd(r, t) is observed. The static pair-correlation function is in agreement with earlier measurements on argon and krypton.