A Baer duality is a triple (R, RUT, T), consisting of rings R, T and a bimodule RUT faithful on both sides, such that the lattices of submodules ℒ(RR) and ℒ(UT), as well as ℒ(RU) and ℒ(TT), are anti-isomorphic. The theory of Baer duality for commutative rings is developed. Analogously to the Morita duality case, it is shown that any commutative ring with Baer duality has self-duality. The existence of the lattice anti-isomorphisms in a Baer duality implies that all the lattices involved satisfy Grothendieck's condition AB5. It is showed that any AB5 commutative domain has Baer duality. An example of an AB5 commutative ring without Baer duality is given.