I. Introduction. - 1. 1 Vector Bundles. - 1. 2 Harmonic Maps. - 1. 3 A Bochner Type Formula. - 1. 4 Basic Properties of Harmonic Maps. - II. Conservation Law. - 2. 1 Stress-Energy Tensor and Conservation Law. - 2. 2 Monotonicity Formula. - 2. 3 Applications of Conservation Law to Liouville type Theorems. - 2. 4 Further Generalizations. - III. Harmonic Maps and Gauss Maps. - 3. 1 Generalized Gauss Maps. - 3. 2 Cone-like Harmonic Maps. - 3. 3 Generalized Maximum Principle. - 3. 4 Estimates of Image Diameter and its Applications. - 3. 5 Gauss Image of a Space-Like Hypersurface in Minkowski Space. - 3. 6 Gauss Image of a Space-Like Submanifold in Pseudo-Euclidean Space. - IV. Harmonic Maps and Holomorphic Maps. - 4. 1 Partial Energies. - 4. 2 Harmonicity of Holomorphic Maps. - 4. 3 Holomorphicity of Harmonic Maps. - V. Existence Nonexistence and Regularity. - 5. 1 Direct Method of the Calculus of Variations. - 5. 2 Regularity Theorems. - 5. 3 Nonexistence and Existence. - 5. 4 Regularity Results of Harmonic Maps into Positively Curved Manifolds. - VI. Equivariant Harmonic Maps. - 6. 1 Riemannian Submersions and Equivariant Harmonic Maps. - 6. 2 Reduction Theorems. - 6. 3 Equivariant Variational Formulas. - 6. 4 On Harmonic Representatives of ?m(Sm). - 6. 5 Harmonic Maps via Isoparametric Maps. - 6. 6 Harmonic Maps of Projective Spaces. - 6. 7 Equivariant Boundary Value Problems. - References. Language: English