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This is a graduate textbook describing atomic-level kinetics (mechanisms and rates) of thermal energy storage; transport (conduction, convection, and radiation); and transformation (various energy conversions) by principal energy carriers. These carriers are: phonon (lattice vibration wave also treated as quasi-particle), electron (as classical or quantum entity), fluid particle (classical particle with quantum features), and photon (classical electromagnetic wave also as quasi-particle). The approach combines the fundamentals of the following fields: molecular orbitals-potentials, statistical thermodynamics, computational molecular dynamics, quantum energy states, transport theories, solid-state and fluid-state physics, and quantum optics. These are rationally connected to atomic-level heat transfer and thermal energy conversion. This textbook presents a unified theory, over fine-structure/molecular-dynamics/Boltzmann/macroscopic length and time scales, of heat transfer kinetics in terms of transition rates and relaxation times, and modern applications, including nano- and microscale size effects. Numerous examples, illustrations, and homework problems with answers enhance learning.