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In describing transport phenomena, it is vital to build the conservation laws of number, energy, momentum, and angular momentum into the structure of the approximation used to determine the thermodynamic many-particle Green's functions. A method for generating conserving approximations has been developed. This method is based on a consideration, at finite temperature, of the equations of motion obeyed by the one-particle propagator $G$, defined in the presence of a nonlocal external scalar field $U$. Approximations for $G(U)$ are obtained by replacing the ${G}_{2}(U)$ which appears in these equations by various functionals of $G(U)$. If the approximation for ${G}_{2}(U)$ satisfies certain simple symmetry conditions, then the $G(U)$ thus defined obeys all the conservation laws. Furthermore, the two-particle correlation function, generated as ${(\frac{\ensuremath{\delta}G}{\ensuremath{\delta}U})}_{U=0}\ensuremath{\equiv}\ifmmode\pm\else\textpm\fi{}L$, in terms of which all linear transport can be described, will obey all the conservation laws as well as several essential sum rules, such as the longitudinal $f$-sum rule.Several examples of conserving approximations are described. The Hartree approximation, ${G}_{2}(U)=G(U)G(U)$, generates the random-phase approximation for $L$. The Hartree-Fock approximation for $G(U)$ leads to a natural generalization of the random-phase approximation in which hole-particle ladder diagrams are summed. Another conserving approximation for $G(U)$ is obtained by expanding the self-energy to first order in the many-particle scattering matrix $T(U)$. This $T$ is obtained by summing ladder diagrams in which the sides of the ladder are composed of $G(U)'\mathrm{s}$. The resulting $L$ equation, which involves coefficients proportional to ${|T|}^{2}$, is analogous to the linearized version of the usual Boltzmann equation. Finally, in order to obtain a description of collisions in a plasma, the self-energy is expanded to first order in a dynamically shielded potential, ${V}_{s}(U)$. This potential is obtained by summing bubbles composed of two $G(U)'\mathrm{s}$. The resulting $L$ equation is similar in structure to a Boltzmann equation in which the collision cross section is proportional to ${|{V}_{s}|}^{2}$.