These are things named after Élie Cartan (9 April 1869 – 6 May 1951), a French mathematician.

• Cartan calculus
• Cartan connection, Cartan connection applications
• Cartan's criterion
• Cartan decomposition
• Cartan's equivalence method
• Cartan formalism (physics)
• Cartan involution
• Cartan's magic formula
• Cartan relations
  • Cartan map
• Cartan matrix
• Cartan pair
• Cartan subalgebra
• Cartan subgroup
• Cartan's method of moving frames
• Cartan's theorem, a name for the closed-subgroup theorem
• Cartan's theorem, a name for the theorem on highest weights
• Cartan's theorem, a name for Lie's third theorem
• Einstein–Cartan theory
  • Einstein–Cartan–Evans theory
• Cartan–Ambrose–Hicks theorem
• Cartan–Brauer–Hua theorem
• Cartan–Dieudonné theorem
• Cartan–Hadamard manifold
• Cartan–Hadamard theorem
• Cartan–Iwahori decomposition
• Cartan-Iwasawa-Malcev theorem
• Cartan–Kähler theorem
• Cartan–Karlhede algorithm
• Cartan–Weyl theory
  • Cartan–Weyl basis
• Cartan–Killing form
• Cartan–Kuranishi prolongation theorem
• CAT(k) space
• Maurer–Cartan form
• Newton–Cartan theory
• Stokes–Cartan theorem, the generalized fundamental theorem of calculus, proven by Cartan (in its general form), also known as Stokes' theorem although Stokes neither formulated nor proved it.

• Cartan (crater)
• Élie Cartan Prize

Note some are after Henri Cartan, a son of É. Cartan; e.g.,

• Cartan's lemma (potential theory)
• Cartan seminar
• Cartan's theorems A and B
• Cartan–Eilenberg resolution