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Thermal radiation represents a ubiquitous aspect of nature. All thermodynamic resources emit or absorb thermal radiation. The ability to control thermal radiation plays a fundamentally important role in a wide range of energy technology. This book is concerned with the modifications of Boltzmann kinetic equation to be suitable for studying the effect of nonlinear thermal radiation field on gases. This happen by amended the force and collision terms in the Boltzmann equation. Analytic exact solutions of nonlinear systems of partial differential equations with variable coefficients, based on the BGK model equation together with suitable boundary and initial conditions are presented. The kinetic and the irreversible thermodynamic properties of the gases and thermal radiations field are investigated from the molecular viewpoint that has many applications in Nano-Technology, nuclear power plants, gas turbines and the various propulsion devices for aircraft, missiles, satellites, spacevehicle and many amazing applications. This book contains many concepts of thermal radiation heat transfer, thermodynamics and different mathematical methods that help researchers in the relevant topics.