## Compositions of Quadratic FormsThe aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2018) |

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### Contents

Exercises | 5 |

Chapter | 13 |

Appendix Composition algebras | 21 |

Notes | 36 |

Exercises | 46 |

Chapter 3 | 52 |

Exercises | 64 |

Notes | 71 |

Notes | 175 |

Exercises | 196 |

Notes | 202 |

Appendix Hasse principle for divisibility of forms | 218 |

Introduction | 227 |

Appendix More applications of topology to algebra | 252 |

Notes | 264 |

Integer Composition Formulas | 268 |

Appendix A Hermitian forms over C | 81 |

Notes | 89 |

Exercises | 101 |

Chapter 6 | 108 |

Exercises | 116 |

Exercises | 131 |

Exercises | 150 |

Notes | 157 |

Appendix Pfister forms and function fields | 167 |

Appendix A A new proof of Yuzvinskys theorem | 286 |

Chapter 14 | 299 |

Appendix Compositions of quadratic forms a J y | 317 |

Appendix Polynomial maps between spheres | 348 |

Notes | 361 |

Exercises | 375 |

407 | |