This book comprehensively explores the foundations of quasiconformal mappings in the complex plane, especially in view of applications to complex dynamics. Besides playing a crucial role in dynamical systems these mappings have important applications in complex analysis, geometry, topology, potential theory and partial differential equations, functional analysis and calculus of variations, electrostatics and nonlinear elasticity . The work covers standard material suitable for a one-year graduate-level course and extends to more advanced topics, in an accessible way even for students in an initial phase of university studies who have learned the basics of complex analysis at the usual level of a rigorous first one-semester course on the subject. At the frontier of complex analysis with real analysis, quasiconformal mappings appeared in 1859-60 in  the cartography work of A. Tissot, well before the term "quasiconformal" was coined by L. Ahlfors in 1935. The detailed study of these mappi