List of things named after Élie Cartan

• Cartan calculus
• Cartan connection, Cartan connection applications
• Cartan's criterion
• Cartan's equivalence method
• Cartan formalism
• Cartan involution
• Cartan's magic formula
• Cartan matrix
• Cartan subalgebra
• Cartan subgroup
• 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
• Cartan–Ambrose–Hicks theorem
• Cartan–Brauer–Hua theorem
• Cartan–Dieudonné theorem
• Cartan–Hadamard theorem
• Cartan–Iwahori decomposition
• Cartan–Kähler theorem
• Cartan–Karlhede algorithm
• Cartan–Kuranishi prolongation theorem
• CAT space
• Maurer–Cartan form
• Newton–Cartan theory
• Stokes–Cartan's theorem, the generalized fundamental theorem of calculus, proven by Cartan, also known as Stokes' theorem although Stokes neither formulated nor proved it.

• Cartan's lemma
• Cartan seminar
• Cartan's theorems A and B