# Local Fields

p-adic Rings and Their Extensionsp-adic ring background, creation and extensions.

[p-Adic Rings and Their Extensions](PAdicRingsAndTheirExtensions/index-padic-rings-and-their-extensions.md)General p-adic ExtensionsGeneral p-adic extension construction, operations and maximal orders.

[General p-Adic Extensions](GeneralPAdicExtensions/index-general-padic-extensions.md)Power, Laurent and Puiseux SeriesPower, Laurent and Puiseux series ring creation and operations.

[Power, Laurent and Puiseux Series](PowerLaurentAndPuiseuxSeries/index-power-laurent-and-puiseux-series.md)Lazy Power Series RingsLazy power series ring creation, operations and elements.

[Lazy Power Series Rings](LazyPowerSeriesRings/index-lazy-power-series-rings.md)Algebraic Power Series RingsAlgebraic power series ring construction and accessors.

[Algebraic Power Series Rings](AlgebraicPowerSeriesRings/index-algebraic-power-series-rings.md)Valuation RingsValuation ring creation, structure and element operations.

[Valuation Rings](ValuationRings/index-valuation-rings.md)Galois RingsGalois ring creation, operations and elements.

[Galois Rings](GaloisRings/index-galois-rings.md)Newton PolygonsNewton polygon computation and applications to factorisation.

[Newton Polygons](NewtonPolygons/index-newton-polygons.md)Series Rings over p-adic RingsSeries rings over p-adic rings, matrices and modules.

[Series Rings over p-Adic Rings](SeriesRingsOverPAdicRings/index-series-rings-over-padic-rings.md)Local Galois RepresentationsLocal Galois representation functions, invariants and arithmetic.

[Local Galois Representations](LocalGaloisRepresentations/index-local-galois-representations.md)