Many phenomena in social, natural and engineering fields are governed by wave, potential, parabolic heat-conduction, hyperbolic heat-conduction and dual-phase-lagging heat-conduction equations. These equations are not only appropriate for describing heat conduction at various scales, but also the most important mathematical equations in physics. The focus of the present monograph is on these equations: their solution structures, methods of finding their solutions under various supplementary conditions, as well as the physical implication and applications of their solutions. Therefore, the present monograph can serve as a reference for researchers working on heat conduction of macro- and micro-scales as well as on mathematical methods of physics. It can also serve as a text for graduate courses on heat conduction or on mathematical equations in physics.