I am currently reading the book by Professor Jost, "Riemannian geometry and geometric analysis", the last chapter on harmonic maps. It talks mainly about existence and regularity of the theory of harmonic mappings between Riemannian manifolds (with certain constraint on the target manifolds, e.g., non-positive curvature). I wonder whether there is a book with a comprehensive treatment on the theory of harmonic mappings between Riemannian manifolds and with applications in other problems.
Another related question that I would like to know is how many different methods that we have to prove the existence of harmonic mappings from a Riemannian manifolds to a Riemannian manifolds with non-positive curvature. How about the regularity part?
The motivation behind the question is that I would like to study the theory of harmonic mappings between singular metric spaces (e.g. the survey book of Professor Lin Fanghua). I know the earlier works of Korevaar-Schoen and Jost around the 1990s, considering such problems in general metric space setting. Any comments and suggestions are warmly welcome!