The hierarchy of distribution-function kinetic equations for a many-body system is usually derived from the Liouville equation, incorporating the elegance of ensemble theory. In this paper emphasis is placed upon the physics of the interactions among particles and the kinetic equations are obtained by considering the time rate of change of the number of particles in phase space due to the flow of particles over phase-space boundaries. In this treatment the connection with experimental requirements is made clear and the distribution functions are identified with coarse grained space and time averages. This paper deals only with nonrelativistic, classical, structureless particles, although guidelines are given for the general treatment whenever approximations are made. The general approach developed here is used to generate kinetic equations for the one-body, the two-body equal-time, and the two-body different-time distribution functions. The remainder of the paper treats the case of an infinite homogeneous system, with a constant ionic background and only Coulomb interactions between electrons. Effective screening potentials are defined whose efficacy is greatest near thermal equilibrium. The one- and two-body kinetic equations are shown to have conservation properties and are analyzed in an energy-angular momentum phase space. The kinetic equation for the correlation function is analyzed to estimate the phase space region of validity for the truncated adiabatic form. Using the effective potentials, a formal solution for g is obtained which leads to a one-particle kinetic equation with no divergence difficulties that is a Boltzmann equation with a distribution function-dependent cross section. This kinetic equation is shown to have an H-theorem to lowest significant order in the plasma parameter. Two phase-space regions are identified, based upon the influence of the effective potential, and an approximate solution for the distribution function is obtained for each region. This analysis shows that, away from thermal equilibrium, the correlation function has an inverse-power asymptotic behavior rather than exponential. Finally, the one-body kinetic equation is shown to reduce in the appropriate region to the Lenard-Balescu form.