Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book "Rational Extended Thermodynamics beyond the Monatomic Gas" by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. The book represents a valuable resource for applied mathematicians, physicists, and engineers, offering powerful models for many potential applications such as reentering satellites into the atmosphere, semiconductors, and nanoscale phenomena.

1. Introduction and Overview.- 2. 2 Mathematical Structure.- 3.  Waves in Hyperbolic Systems.- 4. RET of Rarefied Monatomic Gas: Non-Relativistic Theory.- 5. Relativistic RET of Rarefied Monatomic Gas.- 6. Macroscopic Theory of Rarefied Polyatomic Gas with 14 Fields.- 7. Molecular ET of Rarefied Polyatomic Gas with 14 Fields.- 8. Relaxation Processes of Molecular Rotation and Vibration: ET15.- 9. Nesting Theory of Many Moments and Maximum Entropy Principle.- 10. Monatomic-Gas Limit in Molecular ET of Polyatomic Gas.- 11. Many Moments with Molecular Rotation and Vibration.- 12. Phenomenological Non linear RET with 6 Fields.- 13. Non linear Molecular ET Theory with 6 Fields.- 14. Non linear ET7 Theory with Molecular Rotational and Vibrational Modes.- 15. Non equilibrium Temperature and Chemical Potential.- 16. Linear Sound Wave in a Rarefied Polyatomic Gas.- 17. Shock Wave in a Polyatomic Gas Analyzed by ET14.- 18 Shock Wave and Subshock Formation Analyzed by ET6.- 19 Steady Flow of aPolyatomic Gas.- 20 Acceleration Wave, K-condition, and Global Existence in ET.- 21 Light Scattering.- 22 Heat Conduction.- 23 Fluctuating Hydrodynamics.- 24 RET of Dense Polyatomic Gas with 6 Fields.- 25 RET of Dense Polyatomic Gas with 7 Fields.- 26 Relativistic Polyatomic Gas.- 27 Many-Moment RET of Relativistic Polyatomic Gas and Classical Optimal Limit.- 28 Multi-Temperature Mixture of Fluids.- 29 Shock Structure in a Macroscopic Model of Binary Mixtures.- 30 Flocking and Thermodynamical Cucker-Smale Model.- 31 Mixture of Dissipative Polyatomic Gases.- 32 Relativistic Mixture of Gases and Relativistic Cucker-Smale Model.- 33 Hyperbolic Parabolic Limit, Maxwellian Iteration.