Table of Contents

Geometric considerations.- Conformal mappings.- Existence theorems for harmonic maps between surfaces.- Uniqueness theorems.- A-priori C1,?-estimates.- A-priori estimates from below for the functional determinant of harmonic diffeomorphisms.- The existence of harmonic diffeomorphisms which solve a Dirichlet problem.- C1,— a priori estimates for arbitrary domains. Non-variational existence proofs.- Harmonic coordinates. C2,— a - priori estimates for harmonic maps.- The existence of harmonic diffeomorphisms between surfaces.- Applications of harmonic maps between surfaces.