The Lagrangian formalism

of Calculus of Variations I.- 1. The First Variation.- 2. Variational Problems with Subsidiary Conditions.- 3. General Variational Formulas.- 4. Second Variation, Excess Function, Convexity.- 5. Weak Minimizers and Jacobi Theory.- 6. Weierstrass Field Theory for One-Dimensional Integrals and Strong Minimizers.- Supplement. Some Facts from Differential Geometry and Analysis.- 1. Euclidean Spaces.- 2. Some Function Classes.- 3. Vector and Covector Fields. Transformation Rules.- 4. Differential Forms.- 6. Mean Curvature and Gauss Curvature.