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Introduction; About this book; 1. Trigonometric series and sets of uniqueness; 2. The algebra A of functions with absolutely convergent fourier series, pseudofunctions and pseudomeasures; 3. Symmetric perfect sets and the Salem-Zygmund theorem; 4. Classification of the complexity of U; 5. The Piatetski-Shapiro hierarchy of U-sets; 6. Decomposing U-sets into simpler sets; 7. The shrinking method, the theorem of Körner and Kaufman, and the solution to the Borel basis problem for U; 8. Extended uniqueness sets; 9. Characterizing Rajchman measures; 10. Sets of resolution and synthesis; List of problems; References; Symbols and Abbreviations; Index.

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