nLab
mathematics

• Structural Foundations with annotated toc of 3 great books with numerous links to related nlab content:

  • Categories and Sheaves

  • Sheaves in Geometry and Logic

  • Higher Topos Theory

• Topology and Geometry

  • geometry (general list), topology (general list)

  • general topology

  • algebraic topology

  • homotopy theory

  • rational homotopy theory

  • differential geometry

  • differential topology

  • algebraic geometry

  • noncommutative algebraic geometry

  • noncommutative geometry (general flavour)

  • higher geometry

  • Lie theory

• Algebra:

  • universal algebra

  • higher algebra

  • group theory (including generalizations)

  • representation theory

  • algebraic approaches to differential calculus

  • homological algebra

  • gebras (co(al)gebras, bi/Hopf-algebr-as/oids…)

• mathematical analysis

  • nonstandard analysis, functional analysis, operator algebras

• discrete mathematics:

  • set theory, category theory

  • graph, directed graph, quiver, order, poset, filter, …