Ordinary and Delay Differential Equations I Elementary Methods for Ordinary Differential Equations of First Order 1. Examples and classification 2. Linear equations 3. Separable equations II Uniqueness and Lipschitz Conditions for Ordinary Differential Equations 4. First order scalar equations 5. Systems of equations 6. Higher order equations 7. Complex solutions 8. A valuable lemma 9. A boundary value problem III The Linear Equation of Order n 10. Constant coefficients (the homogeneous case) 11. Linear independence and Wronskians 12. Constant coefficients (general solution for simple h) 13. Variation of parameters IV Linear Ordinary Differential Systems 14. Some general properties 15. Constant coefficients 16. Oscillations and damping in applications 17. Variation of parameters 18. Matrix norm 19. Matrix exponential 20. Existence of solutions (successive approximations) V Introduction to Delay Differential Equations 21. Examples and the method of steps 22. Some distinguishing features and some “wrong” questions 23. Lipschitz condition and uniqueness VI Existence Theory 24. Ordinary differential systems 25. Systems with bounded delays: notation and uniqueness 26. Systems with bounded delays: existence VII Linear Delay Differential Systems 27. Superposition 28. Constant coefficients 29. Variation of parameters VIII Stability 30. Definitions and examples 31. Lyapunov method for uniform stability 32. Asymptotic stability 33. Linear and quasi linear ordinary differential systems 34. Linear and quasi linear delay differential systems IX Autonomous Ordinary Differential Systems 35. Trajectories and critical points 36. Linear systems of second order 37. Critical points of quasi linear systems of second order 38. Global behavior for some nonlinear examples Appendices 1. Notation for sets functions and derivatives Appendices 2. Some theorems from calculus References Answers and Hints.