With about 4% of the periodicity and nearly the regularity, of Edmond Halley's celestial namesake, kinetic theorists gather in the Black Forest for a weeklong conference. At least so it has been since 1976, when the first of these meetings was convened under the leadership of Helmut Neunzert and Donald Pack. Each of these meetings has been duly reported on in this Journal, and herewith we continue the practice. (For the 1976 meeting, entitled “Mathematical Methods in Transport Theory,” see [I]; for the 1979 and 1982 meetings, entitled as the present one, see [2, 31.) The present meeting convened in the first week of May, and with the expert guidance of our leaders, as well as tolerable weather, met our high expectations of delightful and informative sessions. Research areas covered extensively included Vlasov theory and linear and nonlinear Boltzmann theory, with a few contributions more nearly described as general numerical methods and applicable operator theory. We describe first the Vlasov results.