Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, "twistor methods" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.

Part 1 Introduction: harmonic maps, two dimensional domains, maps into symmetric spaces, flag manifolds, summary of contents. 
Part 2 Homogeneous geometry: generalities, reductive splittings, distinct reductive summands, invariant tensors, the Levi-Civita connection, roots, Noether's theorem. 
Part 3 f-structures and f-holomorphic maps. 
Part 4 f-structures on reductive homogeneous spaces: f-structures and metrics, horizontality, example - SU(n) flag manifolds. 
Part 5 Equi-harmonic maps. 
Part 6 Classification of horizontal f-structures on flag manifolds: algebraic preliminaries, reduction to the irreducible case, characterization of irreducible f-structures I, characterization of irreducible f-structures II, summary and examples. 
Part 7 Integrable f-holomorphic orbits on flags: integrable orbits are hermitian symmetric, orbits in the full flag manifold, case 6.13B., case 6.13A., concluding remarks. 
Part 8 Equi-minimal maps of Riemann surfaces to full flag manifolds: equi-minimal maps are horizontal holomorphic, branched horizontal curves in full flags.

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