Preface Chapter 1.Introduction 1.Kahler geometry 2.Kahler and non-Kahler groups 3.Fundamental groups of compact complex surfaces 4.Complex symplectic non-Kahler manifolds Chapter 2.Fibering Kahler manifolds and Kahler groups 1.The fibration problem 2.The Albanese map and free Abelian representations 3.Fibering over Riemann surfaces 4.Fibering compact complex surfaces Chapter 3.The de Rham fundamental group 1.The de Rham fundamental group and the 1-minimal model 2.Formality of compact Kahler manifolds 3.Applications to the fundamental group and examples 4.The Albanese map and the de Rham fundamental group 5.Non-fibered Kahler groups 6.Mixed Hodge structures on the de Rham fundamental group Chapter 4.L2-cohomology of Kahler groups 1.Introduction 2.Simplicial L2-cohomology and ends 3.de Rham L2-cohomology 4.Fibering Kahler manifolds over D2 5.Fibering Kahler manifolds over Riemann surfaces Chapter 5.Existence theorems for harmonic maps 1.Definitions 2.Hartman's uniqueness theorem 3.The Eells-Sampson theorem 4.Equivariant harmonic maps Chapter 6.Applications of harmonic maps 1.Existence of pluriharmonic maps 2.First applications 3.Period domains 4.The factorisation theorem