Philippe Gille is a Research Director for Centre National de la Recherche Scientifique at Institut Camille Jordan, Lyon. He has written numerous research papers on linear algebraic groups and related structures. Tamás Szamuely is a Research Advisor at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, Budapest and a Professor at the Central European University, Hungary. He is the author of Galois Groups and Fundamental Groups (Cambridge, 2009), also published in the Cambridge Studies in Advanced Mathematics series, as well as numerous research papers.

• 1. Quaternion algebras; 2. Central simple algebras and Galois descent; 3. Techniques from group cohomology; 4. The cohomological Brauer group; 5. Severi–Brauer varieties; 6. Residue maps; 7. Milnor K-theory; 8. The Merkurjev–Suslin theorem; 9. Symbols in positive characteristic; Appendix. A breviary of algebraic geometry; Bibliography; Index.

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Philippe Gille is a Research Director for Centre National de la Recherche Scientifique at Institut Camille Jordan, Lyon. He has written numerous research papers on linear algebraic groups and related structures. Tamás Szamuely is a Research Advisor at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, Budapest and a Professor at the Central European University, Hungary. He is the author of Galois Groups and Fundamental Groups (Cambridge, 2009), also published in the Cambridge Studies in Advanced Mathematics series, as well as numerous research papers.

• 1. Quaternion algebras; 2. Central simple algebras and Galois descent; 3. Techniques from group cohomology; 4. The cohomological Brauer group; 5. Severi–Brauer varieties; 6. Residue maps; 7. Milnor K-theory; 8. The Merkurjev–Suslin theorem; 9. Symbols in positive characteristic; Appendix. A breviary of algebraic geometry; Bibliography; Index.

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Philippe Gille is a Research Director for Centre National de la Recherche Scientifique at Institut Camille Jordan, Lyon. He has written numerous research papers on linear algebraic groups and related structures. Tamás Szamuely is a Research Advisor at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, Budapest and a Professor at the Central European University, Hungary. He is the author of Galois Groups and Fundamental Groups (Cambridge, 2009), also published in the Cambridge Studies in Advanced Mathematics series, as well as numerous research papers.

• 1. Quaternion algebras; 2. Central simple algebras and Galois descent; 3. Techniques from group cohomology; 4. The cohomological Brauer group; 5. Severi–Brauer varieties; 6. Residue maps; 7. Milnor K-theory; 8. The Merkurjev–Suslin theorem; 9. Symbols in positive characteristic; Appendix. A breviary of algebraic geometry; Bibliography; Index.

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