Contents: Some Examples; Linear Problems; Green's Function; Method of Complementary Functions; Method of Adjoints; Method of Chasing; Second Order Equations; Error Estimates in Polynomial Interpolation; Existence and Uniqueness; Picard's and Approximate Picard's Method; Quasilinearization and Approximate Quasilinearization; Best Possible Results: Weight Function Technique; Best Possible Results: Shooting Methods; Monotone Convergence and Further Existence; Uniqueness Implies Existence; Compactness Condition and Generalized Solutions; Uniqueness Implies Uniqueness; Boundary Value Functions; Topological Methods; Best Possible Results: Control Theory Methods; Matching Methods; Maximal Solutions; Maximum Principle; Infinite Interval Problems; Equations with Deviating Arguments;