Table of Contents Chapter 1.Infinite Galois Theory and Profinite Groups Chapter 2.Valuations and Linear Disjointness Chapter 3.Algebraic Function Fields of One Variable Chapter 4.The Riemann Hypothesis for Function Fields Chapter 5.Plane Curves Chapter 6.The Chebotarev Density Theorem Chapter 7.Ultraproducts Chapter 8.Decision Procedures Chapter 9.Algebraically Closed Fields Chapter 10.Elements of Algebraic Geometry Chapter 11.Pseudo Algebraically Closed Fields Chapter 12.Hilbertian Fields Chapter 13.The Classical Hilbertian Fields Chapter 14.Nonstandard Structures Chapter 15.Nonstandard Approach to Hilbert’s Irreducibility Theorem Chapter 16.Galois Groups over Hilbertian Fields Chapter 17.Free Profinite Groups Chapter 18.The Haar Measure Chapter 19.Effective Field Theory and Algebraic Geometry Chapter 20.The Elementary Theory of e-Free PAC Fields Chapter 21.Problems of Arithmetical Geometry Chapter 22.Projective Groups and Frattini Covers Chapter 23.PAC Fields and Projective Absolute Galois Groups Chapter 24.Frobenius Fields Chapter 25.Free Profinite Groups of Infinite Rank Chapter 26.Random Elements in Free Profinite Groups Chapter 27.Omega-Free PAC Fields Chapter 28.Undecidability Chapter 29.Algebraically Closed Fields with Distinguished Automorphisms Chapter 30.Galois Stratification Chapter 31.Galois Stratification over Finite Fields Chapter 32.Problems of Field Arithmetic Table of Contents References Index