(1):
(a.) To make stable or firm; to fix immovably or firmly; to set (a thing) in a place and make it stable there; to settle; to confirm.
(2):
(a.) To appoint or constitute for permanence, as officers, laws, regulations, etc.; to enact; to ordain.
(3):
(a.) To originate and secure the permanent existence of; to found; to institute; to create and regulate; - said of a colony, a state, or other institutions.
(4):
(a.) To secure public recognition in favor of; to prove and cause to be accepted as true; as, to establish a fact, usage, principle, opinion, doctrine, etc.
(5):
(a.) To set up in business; to place advantageously in a fixed condition; - used reflexively; as, he established himself in a place; the enemy established themselves in the citadel.