The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory.This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction.In addition to chapters on specialization theory, generic splitting theory and their applications, the book contains a final chapter containing research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.

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