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Groups as Galois Groups
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Table of Contents

Part 1. The Basic Rigidity Criteria: 1. Hilbert's irreducibility theorem; 2. Finite Galois extensions of C (x); 3. Descent of base field and the rigidity criterion; 4. Covering spaces and the fundamental group; 5. Riemann surfaces and their functional fields; 6. The analytic version of Riemann's existence theorem; Part II. Further Directions: 7. The descent from C to k; 8. Embedding problems: braiding action and weak rigidity; Moduli spaces for covers of the Riemann sphere; Patching over complete valued fields.

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Develops the mathematical background and recent results on the Inverse Galois Problem.

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From the hardback review: 'I highly recommend this book to all readers who like to learn this aspect of Galois theory, those who like to give a course on Galois theory and those who like to see how different mathematical methods as analysis, Riemann surface theory and group theory yield a nice algebraic result.' Translated from Martin Epkenhans, Zentralblatt fur Mathematiche From the hardback review: '... a very helpful introduction into an active research area, recommended for graduate students and anyone interested in recent progress in the inverse Galois problem.' B. H. Matzat, Bulletin of London Mathmatical Society

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