A pulsed supersonic molecular beam apparatus has been constructed for the investigation of atomic and molecular van der Waals clusters. The apparatus was characterized by investigating supersonic beam intensities as a function of reservoir pressure and nozzle to skimmer separation, and by measuring supersonic beam speed distributions for various monatomic and diatomic gases and binary monatomic gas mixtures using time-of-flight methods. A new technique for deconvolving badly convoluted time-of-flight data was developed and successfully applied to the deconvolution of time-of-flight waveforms measured for unchopped pulsed supersonic beams of argon, krypton, CHCl₃ and CH₃Cl. Size distributions of van der Waals cluster species were investigated for supersonic expansions of pure argon and for seeded helium expansions containing 8O₂, N₂O and H₂O, NO and NO₂ and NH₃. Appearance potentials of the cluster ions (CO₂)n⁺, (N₂O) n⁺ (2 ≤ n ≤ 4) and (NH₃)nH⁺ (1 ≤ n ≤ 8), and the cluster ion fragments (N₂O∙O)+ and (N₂O∙NO)+ have been determined by electron impact ionization of neutral clusters formed in the supersonic beam. The measured appearance potential data were used to estimate cluster ion binding energies, and possible mechanisms for the formation of the cluster fragment ions (N₂O∙O)+ and (N₂O∙NO)+ are discussed. Computational procedures have been developed for the calculation of supersonic beam properties as a function of distance along the expansion axis. Collision frequency, flow velocity, particle density, mean free path, and axial and radial temperatures in supersonic atomic and homonuclear diatomic beams have been calculated for various species using realistic interaction potentials and collision cross sections obtained from scattering theory. A simple approach to the estimation of rotational relaxation times and collision numbers in supersonic expansions was developed and used to calculate rotational relaxation times and rotational collision numbers for H₂, N ₂, O ₂ and Cl₂. A sophisticated direct simulation Monte Carlo procedure was devised for the investigation of rotational relaxation in small molecules. The devised relaxation model has been used to calculate rotational relaxation data for the homonuclear diatomic molecules H₂, N₂, O ₂ and Cl₂, and for the polyatomic species CO₂, OCS, NH₃, CH₄, CH₃Cl and C₂H₄. Results obtained using the Monte Carlo procedure were used to investigate the breakdown of translational and rotational equilibrium in supersonic expansions of CO₂, OCS and CH₃Cl.