With the advent of sophisticated computer technology and the development of efficient computational algorithms, numerical modeling of complex multicomponent laminar reacting flows has emerged as an increasingly popular and firmly established area of scientific research. Progress in this area aims at obtaining better resolved and more accurate solutions of specific technological problems in less computer time. Therefore, it strongly relies upon the ability of evaluating fundamental parameters appearing in the physical models. Transport properties constitute a typical example of the above characterization. Evaluating transport coefficients of dilute polyatomic gas mixtures is often critical in many engineering applications, including chemical reactors, hypersonic flows, comb- tion phenomena, and chemical vapor deposition. Using the kinetic theory of dilute polyatomic gas mixtures as a starting point, this book offers a systematic development of a mathematical and numerical theory for the evaluation of transport properties in dilute polyatomic gas mixtures. The present investigation is not specifically.about the kinetic theory of gases, for which there are plenty of excellent and thoroughly do- mented textbooks; it is rather geared toward the development of new, efficient, and general algorithms with which to evaluate transport properties of dilute polyatomic gas mixtures at a reasonable computational cost.