> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/900-index/lists/list-of-math-theories.md).

# List of mathematical theories

<https://en.wikipedia.org/wiki/List_of_mathematical_theories>

* Sets
  * Set theory

    <https://en.wikipedia.org/wiki/Set_theory>
  * Theory of relations

    <https://en.wikipedia.org/wiki/Finitary_relation>
  * Order theory

    <https://en.wikipedia.org/wiki/Order_theory>
  * Domain theory

    <https://en.wikipedia.org/wiki/Domain_theory>
  * 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>
      * *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>
      * *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>
      * *Geometric function theory*, the study of geometric properties of analytic functions.

        <https://en.wikipedia.org/wiki/Geometric_function_theory>
* Algebra
  * Theory of equations

    <https://en.wikipedia.org/wiki/Theory_of_equations>
  * Representation theory

    <https://en.wikipedia.org/wiki/Representation_theory>
  * Semigroup theory

    <https://en.wikipedia.org/wiki/Semigroup_theory>
  * Group theory

    <https://en.wikipedia.org/wiki/Group_theory>
  * Field theory

    <https://en.wikipedia.org/wiki/Field_theory_(mathematics>)
  * Ring theory

    <https://en.wikipedia.org/wiki/Ring_theory>
* Proof theory

  <https://en.wikipedia.org/wiki/Proof_theory>
* Type theory

  <https://en.wikipedia.org/wiki/Type_theory>
* 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>
  * Renewal theory

    <https://en.wikipedia.org/wiki/Renewal_theory>
* Networks, Operations research
  * Network theory

    <https://en.wikipedia.org/wiki/Number_theory>
  * Queue theory

    <https://en.wikipedia.org/wiki/Queue_theory>
* Quantum physics
  * Quantum theory

    <https://en.wikipedia.org/wiki/Quantum_mechanics>
  * Twistor theory

    <https://en.wikipedia.org/wiki/Twistor_theory>
* Topology
  * Surgery theory

    <https://en.wikipedia.org/wiki/Surgery_theory>
  * Topos theory

    <https://en.wikipedia.org/wiki/Topos_theory>
  * Homology theory

    <https://en.wikipedia.org/wiki/Homology_theory>
  * Homotopy theory

    <https://en.wikipedia.org/wiki/Homotopy_theory>
  * 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/Almgren%E2%80%93Pitts_min-max_theory> <https://en.wikipedia.org/wiki/Approximation_theory> <https://en.wikipedia.org/wiki/Asymptotic_theory> <https://en.wikipedia.org/wiki/Automata_theory> <https://en.wikipedia.org/wiki/Bifurcation_theory> <https://en.wikipedia.org/wiki/Braid_theory> <https://en.wikipedia.org/wiki/Brill%E2%80%93Noether_theory> <https://en.wikipedia.org/wiki/Catastrophe_theory> <https://en.wikipedia.org/wiki/Category_theory> <https://en.wikipedia.org/wiki/Chaos_theory> <https://en.wikipedia.org/wiki/Character_theory> <https://en.wikipedia.org/wiki/Choquet_theory> <https://en.wikipedia.org/wiki/Class_field_theory> <https://en.wikipedia.org/wiki/Coding_theory> <https://en.wikipedia.org/wiki/Cohomology_theory> <https://en.wikipedia.org/wiki/Computation_theory> <https://en.wikipedia.org/wiki/Deformation_theory> <https://en.wikipedia.org/wiki/Dimension_theory> <https://en.wikipedia.org/wiki/Distribution_(mathematics>) <https://en.wikipedia.org/wiki/Elimination_theory> <https://en.wikipedia.org/wiki/Extremal_graph_theory> <https://en.wikipedia.org/wiki/Galois_theory> <https://en.wikipedia.org/wiki/Game_theory> <https://en.wikipedia.org/wiki/Graph_theory> <https://en.wikipedia.org/wiki/Grothendieck%27s_Galois_theory> <https://en.wikipedia.org/wiki/Hodge_theory> <https://en.wikipedia.org/wiki/Information_theory> <https://en.wikipedia.org/wiki/Invariant_theory> <https://en.wikipedia.org/wiki/K-theory> <https://en.wikipedia.org/wiki/Knot_theory> <https://en.wikipedia.org/wiki/L-theory> <https://en.wikipedia.org/wiki/Local_class_field_theory> <https://en.wikipedia.org/wiki/M-theory> <https://en.wikipedia.org/wiki/Matrix_(mathematics>) <https://en.wikipedia.org/wiki/Measure_theory> <https://en.wikipedia.org/wiki/Model_theory> <https://en.wikipedia.org/wiki/Module_theory> <https://en.wikipedia.org/wiki/Network_theory> <https://en.wikipedia.org/wiki/Nevanlinna_theory> <https://en.wikipedia.org/wiki/Obstruction_theory> <https://en.wikipedia.org/wiki/Operator_theory> <https://en.wikipedia.org/wiki/Percolation_theory> <https://en.wikipedia.org/wiki/Perturbation_theory> <https://en.wikipedia.org/wiki/Scheme_theory> <https://en.wikipedia.org/wiki/Seiberg%E2%80%93Witten_theory> <https://en.wikipedia.org/wiki/Sheaf_(mathematics>) <https://en.wikipedia.org/wiki/Singularity_theory> <https://en.wikipedia.org/wiki/Spectral_theory> <https://en.wikipedia.org/wiki/String_theory> <https://en.wikipedia.org/wiki/Transcendental_number_theory>