# Global Fields

Number FieldsDefining number fields, elements and embeddings.

[Number Fields](NumberFields/index-number-fields.md)Quadratic FieldsQuadratic field creation, structure and element operations.

[Quadratic Fields](QuadraticFields/index-quadratic-fields.md)Cyclotomic FieldsCyclotomic field creation, structure and element operations.

[Cyclotomic Fields](CyclotomicFields/index-cyclotomic-fields.md)Number Fields and OrdersOrders in number fields: creation, arithmetic and printing.

[Number Fields and Orders](NumberFieldsAndOrders/index-number-fields-and-orders.md)Galois Groups and AutomorphismsAutomorphism groups, Galois groups, subfields and cohomology.

[Galois Groups and Automorphisms](GaloisGroupsAndAutomorphisms/index-galois-groups-and-automorphisms.md)Class Field TheoryAbelian extensions, ray class fields and Galois module structure.

[Class Field Theory](ClassFieldTheory/index-class-field-theory.md)Étale AlgebrasÉtale algebra construction, attributes and homomorphisms.

[Étale Algebras](EtaleAlgebras/index-etale-algebras.md)Dirichlet and Hecke CharactersDirichlet and Hecke character construction and properties.

[Dirichlet and Hecke Characters](DirichletAndHeckeCharacters/index-dirichlet-and-hecke-characters.md)Algebraically Closed FieldsAlgebraically closed field representation, structure and creation.

[Algebraically Closed Fields](AlgebraicallyClosedFields/index-algebraically-closed-fields.md)Rational Function FieldsRational function field creation, operations and elements.

[Rational Function Fields](RationalFunctionFields/index-rational-function-fields.md)Algebraic Function FieldsAlgebraic function field creation and structural invariants.

[Algebraic Function Fields](AlgebraicFunctionFields/index-algebraic-function-fields.md)Class Field Theory for Global Function FieldsClass groups, abelian extensions and Witt rings for function fields.

[Class Field Theory for Global Function Fields](ClassFieldTheoryForGlobalFunctionFields/index-class-field-theory-for-global-function-fields.md)Artin RepresentationsArtin representation functions, invariants and arithmetic.

[Artin Representations](ArtinRepresentations/index-artin-representations.md)