  We construct several families of Artin-Schelter regular algebras of global
dimension four using double Ore extension and then prove that all these
algebras are strongly noetherian, Auslander regular, Koszul and Cohen-Macaulay
domains. Many regular algebras constructed in the paper are new and are not
isomorphic to either a normal extension or an Ore extension of an
Artin-Schelter regular algebra of global dimension three.
