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1. The representation theory of Cassels 2. Multiplicative quadratic forms 3. The level of fields, rings and topological spaces 4. Hilbert's homogeneous nullstellensatz 5. Tsen-Lang theory 6. Hilbert's 17th problem 7. The Pythagoras number 8. The u-invariant 9. Systems of quadratic forms 10. The level of projective spaces.