Webster's Dictionary 
(1): (n.) A school or place of training in which some special art is taught; as, the military academy at West Point; a riding academy; the Academy of Music.
(2): (n.) A society of learned men united for the advancement of the arts and sciences, and literature, or some particular art or science; as, the French Academy; the American Academy of Arts and Sciences; academies of literature and philology.
(3): (n.) A place of training; a school.
(4): (n.) An institution for the study of higher learning; a college or a university. Popularly, a school, or seminary of learning, holding a rank between a college and a common school.
(5): (n.) A garden or grove near Athens (so named from the hero Academus), where Plato and his followers held their philosophical conferences; hence, the school of philosophy of which Plato was head.
The Nuttall Encyclopedia 
A public shady park or place of groves near Athens, where Plato taught his philosophy and whence his school derived its name, of which there are three branches, the Old , the Middle , and the New , represented respectively by Plato himself, Arcesilaos, and Carneades. The French Academy , of forty members, was founded by Richelieu in 1635, and is charged with the interests of the French language and literature, and in particular with the duty of compiling an authoritative dictionary of the French language. Besides these, there are in France other four with a like limited membership in the interest of other departments of science and art, all now associated in the Institute of France , which consists in all of 229 members. There are similar institutions in other states of Europe, all of greater or less note.