Harmonic maps between Riemannian manifolds are solutions of systems of partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, delta-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kahlerian manifolds. Standard references for this subject are two reports, published in 1978 and 1988 by James Eells and Luc Lemaire. This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a source of reference, providing an organized exposition of results spread throughout more than 800 papers.