Basic Quadratic Forms
Larry J. Gerstein · Graduate studies in mathematics · 2008
A brief classical introduction Quadratic spaces and lattices Valuations, local fields, and $p$-adic numbers Quadratic spaces over $\mathbb{Q}_p$ Quadratic spaces over $\mathbb{Q}$ Lattices over principal ideal domains Initial integral results Local classification of lattices The local-global approach to lattices Lattices over $\mathbb{F}_q[x]$ Applications to cryptography Further reading Bibliography Index.