The authors present a general and self-contained theory of iterative algorithms for evaluating transport coefficients in multicomponent, and especially dilute polyatomic gas mixtures thus filling a gap left by other books that give preference to pure (mostly monatomic) gases and to binary mixtures. Approximate expressions for the transport coefficients are rigorously derived from the kinetic theory. These can be readily used, at a reduced computational cost, in numerical models. Hence, the present algorithms will be of extensive interest in theoretical calculations and numerical modeling for fluid mechanics, combustion, crystal growth, and other engineering applications. The material is covered rigorously and comprehensively, and every mathematical step is carefully explained.