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Preface. Conventions, Notations Part 1. Introduction 1. Idealization 2. Standardization and Transfer 3. Real Numbers and Numerical Functions 4. Continuity 5. Differentiability 6. Integration Part 2. 7. Invariant Means 8. Approximation of Functions 9. Differential Equations 10. Perturbation of a Green Function 11. Invariant Subspaces Problem Indications for Exercises. Solutions of Exercises Bibliography. Index Basic Principles of NSA. IST Axioms for NSA