Symmetric Bilinear Forms

I. Basic Concepts.- II. Symmetric Inner Product Spaces over Z.- III. Inner Product Spaces over a Field.- IV. Discrete Valuations and Dedekind Domains.- V. Some Examples.- Appendix 1. Quadratic Forms.- Appendix 2. Hermitian Forms.- Appendix 3. The Hasse-Minkowski Theorem.- Appendix 4. Gauss Sums, the Signature mod 8, and Quadratic Reciprocity.- Appendix 5. The Leech Lattice, and Other Lattices in Dimension 24.- Chronological Table.- References.- Special Notations.