Synopsis
1. Abelian Groups and Character Sums.- 2. Introduction to Sumsets.- 3. Simple Results for Torsion-Free Abelian Groups.- 4. Basic Results for Sumsets with an Infinite Summand.- 5. The Pigeonhole and Multiplicity Bounds.- 6. Periodic Sets and Kneser's Theorem.- 7. Compression, Complements and the 3k-4 Theorem.- 8. Additive Energy.- 9. Kemperman's Critical Pair Theory.- 10. Zero-Sums, Setpartitions and Subsequence Sums.- 11. Long Zero-Sum Free Sequences over Cyclic Groups.- 12. Pollard's Theorem for General Abelian Groups.- 13. The DeVos-Goddyn-Mohar Theorem.- 14. The Partition Theorem I.- 15. The Partition Theorem II.- 16. The Ψ-Weighted Gao Theorem.- 17. Group Algebras.- 18. Character and Linear Algebraic Methods.- 19. Character Sum and Fourier Analytic Methods.- 20. Freiman Homomorphisms Revisited.- 21. The Isoperimetric Method.- 22. The Polynomial Method.- Index.
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