# List of mathematical theories

[https://en.wikipedia.org/wiki/List\_of\_mathematical\_theories](https://en.wikipedia.org/wiki/List_of_mathematical_theories)

* Sets
  *   Set theory

      [https://en.wikipedia.org/wiki/Set\_theory](https://en.wikipedia.org/wiki/Set_theory)
  *   Theory of relations

      [https://en.wikipedia.org/wiki/Finitary\_relation](https://en.wikipedia.org/wiki/Finitary_relation)
  *   Order theory

      [https://en.wikipedia.org/wiki/Order\_theory](https://en.wikipedia.org/wiki/Order_theory)
  *   Domain theory

      [https://en.wikipedia.org/wiki/Domain\_theory](https://en.wikipedia.org/wiki/Domain_theory)
  *   Function theory

      [https://en.wikipedia.org/wiki/Function\_theory](https://en.wikipedia.org/wiki/Function_theory)

      * Function theory may refer to:
        *   _Theory of functions of a real variable_, the traditional name of **real analysis**, a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable.

            [https://en.wikipedia.org/wiki/Real\_analysis](https://en.wikipedia.org/wiki/Real_analysis)
        *   _Theory of functions of a complex variable_, the historical name for **complex analysis**, the branch of mathematical analysis that investigates functions of complex numbers.

            [https://en.wikipedia.org/wiki/Complex\_analysis](https://en.wikipedia.org/wiki/Complex_analysis)
        *   _Constructive function theory_, the study of the connection between the smoothness of a function and its degree of approximation.

            [https://en.wikipedia.org/wiki/Constructive\_function\_theory](https://en.wikipedia.org/wiki/Constructive_function_theory)
        *   _Geometric function theory_, the study of geometric properties of analytic functions.

            [https://en.wikipedia.org/wiki/Geometric\_function\_theory](https://en.wikipedia.org/wiki/Geometric_function_theory)
* Algebra
  *   Theory of equations

      [https://en.wikipedia.org/wiki/Theory\_of\_equations](https://en.wikipedia.org/wiki/Theory_of_equations)
  *   Representation theory

      [https://en.wikipedia.org/wiki/Representation\_theory](https://en.wikipedia.org/wiki/Representation_theory)
  *   Semigroup theory

      [https://en.wikipedia.org/wiki/Semigroup\_theory](https://en.wikipedia.org/wiki/Semigroup_theory)
  *   Group theory

      [https://en.wikipedia.org/wiki/Group\_theory](https://en.wikipedia.org/wiki/Group_theory)
  *   Field theory

      [https://en.wikipedia.org/wiki/Field\_theory\_(mathematics](https://en.wikipedia.org/wiki/Field_theory_\(mathematics))
  *   Ring theory

      [https://en.wikipedia.org/wiki/Ring\_theory](https://en.wikipedia.org/wiki/Ring_theory)
*   Proof theory

    [https://en.wikipedia.org/wiki/Proof\_theory](https://en.wikipedia.org/wiki/Proof_theory)
*   Type theory

    [https://en.wikipedia.org/wiki/Type\_theory](https://en.wikipedia.org/wiki/Type_theory)
* Recursion theory [https://en.wikipedia.org/wiki/Recursion\_theory](https://en.wikipedia.org/wiki/Recursion_theory)
* Coding theory
* Number theory
* Automata theory
* Asymptotic theory
* Graph theory
* Computation theory
* Information theory
* Category theory
* Chaos theory
* Dimension theory
* Game theory
* Knot theory
* Matrix theory
* Measure theory
* Model theory
* Module theory
* Operator theory
* String theory
* Transcendental number theory
* Algebraic K-theory
* Almgren-Pitts min-max theory
* Approximation theory
* Bifurcation theory
* Braid theory
* Brill-Noether theory
* Catastrophe theory
* Character theory
* Choquet theory
* Class field theory
* Cohomology theory
* Deformation theory
* Distribution theory
* Elimination theory
* Equational theory
* Extremal graph theory
* Galois theory
* Grothendieck's Galois theory
* Hodge theory
* Invariant theory
* K-theory
* L-theory
* Local class field theory
* M-theory
* Nevanlinna theory
* Obstruction theory
* Percolation theory
* Perturbation theory
* Scheme theory
* Seiberg-Witten theory
* Sheaf theory
* Singularity theory
* Spectral theory
* Probability
  *   Probability theory

      [https://en.wikipedia.org/wiki/Probability\_theory](https://en.wikipedia.org/wiki/Probability_theory)
  *   Renewal theory

      [https://en.wikipedia.org/wiki/Renewal\_theory](https://en.wikipedia.org/wiki/Renewal_theory)
* Networks, Operations research
  *   Network theory

      [https://en.wikipedia.org/wiki/Number\_theory](https://en.wikipedia.org/wiki/Number_theory)
  *   Queue theory

      [https://en.wikipedia.org/wiki/Queue\_theory](https://en.wikipedia.org/wiki/Queue_theory)
* Quantum physics
  *   Quantum theory

      [https://en.wikipedia.org/wiki/Quantum\_mechanics](https://en.wikipedia.org/wiki/Quantum_mechanics)
  *   Twistor theory

      [https://en.wikipedia.org/wiki/Twistor\_theory](https://en.wikipedia.org/wiki/Twistor_theory)
* Topology
  *   Surgery theory

      [https://en.wikipedia.org/wiki/Surgery\_theory](https://en.wikipedia.org/wiki/Surgery_theory)
  *   Topos theory

      [https://en.wikipedia.org/wiki/Topos\_theory](https://en.wikipedia.org/wiki/Topos_theory)
  *   Homology theory

      [https://en.wikipedia.org/wiki/Homology\_theory](https://en.wikipedia.org/wiki/Homology_theory)
  *   Homotopy theory

      [https://en.wikipedia.org/wiki/Homotopy\_theory](https://en.wikipedia.org/wiki/Homotopy_theory)
  *   Morse theory

      [https://en.wikipedia.org/wiki/Morse\_theory](https://en.wikipedia.org/wiki/Morse_theory)

## Wikipedia links to mathematical theories

[https://en.wikipedia.org/wiki/Algebraic\_K-theory](https://en.wikipedia.org/wiki/Algebraic_K-theory) [https://en.wikipedia.org/wiki/Almgren%E2%80%93Pitts\_min-max\_theory](https://en.wikipedia.org/wiki/Almgren%E2%80%93Pitts_min-max_theory) [https://en.wikipedia.org/wiki/Approximation\_theory](https://en.wikipedia.org/wiki/Approximation_theory) [https://en.wikipedia.org/wiki/Asymptotic\_theory](https://en.wikipedia.org/wiki/Asymptotic_theory) [https://en.wikipedia.org/wiki/Automata\_theory](https://en.wikipedia.org/wiki/Automata_theory) [https://en.wikipedia.org/wiki/Bifurcation\_theory](https://en.wikipedia.org/wiki/Bifurcation_theory) [https://en.wikipedia.org/wiki/Braid\_theory](https://en.wikipedia.org/wiki/Braid_theory) [https://en.wikipedia.org/wiki/Brill%E2%80%93Noether\_theory](https://en.wikipedia.org/wiki/Brill%E2%80%93Noether_theory) [https://en.wikipedia.org/wiki/Catastrophe\_theory](https://en.wikipedia.org/wiki/Catastrophe_theory) [https://en.wikipedia.org/wiki/Category\_theory](https://en.wikipedia.org/wiki/Category_theory) [https://en.wikipedia.org/wiki/Chaos\_theory](https://en.wikipedia.org/wiki/Chaos_theory) [https://en.wikipedia.org/wiki/Character\_theory](https://en.wikipedia.org/wiki/Character_theory) [https://en.wikipedia.org/wiki/Choquet\_theory](https://en.wikipedia.org/wiki/Choquet_theory) [https://en.wikipedia.org/wiki/Class\_field\_theory](https://en.wikipedia.org/wiki/Class_field_theory) [https://en.wikipedia.org/wiki/Coding\_theory](https://en.wikipedia.org/wiki/Coding_theory) [https://en.wikipedia.org/wiki/Cohomology\_theory](https://en.wikipedia.org/wiki/Cohomology_theory) [https://en.wikipedia.org/wiki/Computation\_theory](https://en.wikipedia.org/wiki/Computation_theory) [https://en.wikipedia.org/wiki/Deformation\_theory](https://en.wikipedia.org/wiki/Deformation_theory) [https://en.wikipedia.org/wiki/Dimension\_theory](https://en.wikipedia.org/wiki/Dimension_theory) [https://en.wikipedia.org/wiki/Distribution\_(mathematics](https://en.wikipedia.org/wiki/Distribution_\(mathematics)) [https://en.wikipedia.org/wiki/Elimination\_theory](https://en.wikipedia.org/wiki/Elimination_theory) [https://en.wikipedia.org/wiki/Extremal\_graph\_theory](https://en.wikipedia.org/wiki/Extremal_graph_theory) [https://en.wikipedia.org/wiki/Galois\_theory](https://en.wikipedia.org/wiki/Galois_theory) [https://en.wikipedia.org/wiki/Game\_theory](https://en.wikipedia.org/wiki/Game_theory) [https://en.wikipedia.org/wiki/Graph\_theory](https://en.wikipedia.org/wiki/Graph_theory) [https://en.wikipedia.org/wiki/Grothendieck%27s\_Galois\_theory](https://en.wikipedia.org/wiki/Grothendieck's_Galois_theory) [https://en.wikipedia.org/wiki/Hodge\_theory](https://en.wikipedia.org/wiki/Hodge_theory) [https://en.wikipedia.org/wiki/Information\_theory](https://en.wikipedia.org/wiki/Information_theory) [https://en.wikipedia.org/wiki/Invariant\_theory](https://en.wikipedia.org/wiki/Invariant_theory) [https://en.wikipedia.org/wiki/K-theory](https://en.wikipedia.org/wiki/K-theory) [https://en.wikipedia.org/wiki/Knot\_theory](https://en.wikipedia.org/wiki/Knot_theory) [https://en.wikipedia.org/wiki/L-theory](https://en.wikipedia.org/wiki/L-theory) [https://en.wikipedia.org/wiki/Local\_class\_field\_theory](https://en.wikipedia.org/wiki/Local_class_field_theory) [https://en.wikipedia.org/wiki/M-theory](https://en.wikipedia.org/wiki/M-theory) [https://en.wikipedia.org/wiki/Matrix\_(mathematics](https://en.wikipedia.org/wiki/Matrix_\(mathematics)) [https://en.wikipedia.org/wiki/Measure\_theory](https://en.wikipedia.org/wiki/Measure_theory) [https://en.wikipedia.org/wiki/Model\_theory](https://en.wikipedia.org/wiki/Model_theory) [https://en.wikipedia.org/wiki/Module\_theory](https://en.wikipedia.org/wiki/Module_theory) [https://en.wikipedia.org/wiki/Network\_theory](https://en.wikipedia.org/wiki/Network_theory) [https://en.wikipedia.org/wiki/Nevanlinna\_theory](https://en.wikipedia.org/wiki/Nevanlinna_theory) [https://en.wikipedia.org/wiki/Obstruction\_theory](https://en.wikipedia.org/wiki/Obstruction_theory) [https://en.wikipedia.org/wiki/Operator\_theory](https://en.wikipedia.org/wiki/Operator_theory) [https://en.wikipedia.org/wiki/Percolation\_theory](https://en.wikipedia.org/wiki/Percolation_theory) [https://en.wikipedia.org/wiki/Perturbation\_theory](https://en.wikipedia.org/wiki/Perturbation_theory) [https://en.wikipedia.org/wiki/Scheme\_theory](https://en.wikipedia.org/wiki/Scheme_theory) [https://en.wikipedia.org/wiki/Seiberg%E2%80%93Witten\_theory](https://en.wikipedia.org/wiki/Seiberg%E2%80%93Witten_theory) [https://en.wikipedia.org/wiki/Sheaf\_(mathematics](https://en.wikipedia.org/wiki/Sheaf_\(mathematics)) [https://en.wikipedia.org/wiki/Singularity\_theory](https://en.wikipedia.org/wiki/Singularity_theory) [https://en.wikipedia.org/wiki/Spectral\_theory](https://en.wikipedia.org/wiki/Spectral_theory) [https://en.wikipedia.org/wiki/String\_theory](https://en.wikipedia.org/wiki/String_theory) [https://en.wikipedia.org/wiki/Transcendental\_number\_theory](https://en.wikipedia.org/wiki/Transcendental_number_theory)
