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Part I. Algebra: 1. An informal introduction 2. What is a spectral sequence? 3. Tools and examples Part II. Topology: 4. Topological background 5. The Leray-Serre spectral sequence I 6. The Leray-Serre spectral sequence II 7. The Eilenberg-Moore spectral sequence I 8. The Eilenberg-Moore spectral sequence II 9. The Adams spectral sequence 10. The Bockstein spectral sequence Part III. Sins of Omission: 11. Spectral sequences in algebra, algebraic geometry and algebraic K-theory 12. More spectral sequences in topology.