Daniel B. Shapiro, Compositions of Quadratic Forms, 2000. 24 x 17 cm. 417 pages. Hardcover.
ISBN 978-3-11-012629-7 Series: de Gruyter Expositions in Mathematics 33.
Here PDF files for this book.
Intro.pdf Introduction.
section 2.pdf Chapters 1 – 5.
section 3.pdf Chapters 5 – 10.
section 4.pdf Chapters 10 – 14.
section 5.pdf Chapters 14 – 16 and Bibliography.
section 6.pdf (better Chapter 13)
section 7.pdf (Bibliography)
Update: The paper Constructions was posted to arXiv.org in 2017. This sharpens the “doubling construction” mentioned in earlier references.