The book treats the problem of single- and two-phase heat transfer in micro-channels. We consider the effect of wall roughness on energy dissipation, axial heat conduction, operating parameters corresponding to stable and unstable flow and steady and unsteady flow with distinct interface. In the book we use our own results on a number of problems related to flow and heat transfer, as well as those of numerous theoretical and experimental investigations published in current literature. The presented materials are easily comprehensible to engineers and engineering students with some graduate-level familiarity of fluid mechanics and the theory of heat transfer.