Algebras:
commutative algebras	non-commutative algebras
Typical examples:
Polynomial algebra R[X1,X2,X3]	Exterior algebras generated by e1,e2,e3
(the polynomial functions on R3)	(the differential forms on R3)
Commutativity XiXj - XjXi = 0	Anti-commutativity eiej + ejei = 0
infinite dimensional over R	finite dimensional over R
"Koszul duality" These algebras determine each other!