Located on the banks of the Ilissus in an eastern suburb of Athens, the Lyceum was a gymnasium with covered walks named after the neighboring temple of Lycian Apollo. In 335 B.C. Aristotle established a school and research institute in the Lyceum under the patronage of the Macedonian proconsul, Antipater. Each of the covered walks adjoining the Lyceum was called a peripatos; hence, the term peripatetikos came to mean "given to waking about, especially while teaching." Since Aristotle frequently conducted his teaching in this manner, he and disciples were known as the Peripatetics.
The epithet of Apollo from which "lyceum" derives, is of uncertain origin; it may have evolved from lycos, wolf-slaying, Lycia, a place in the southern reaches of Asia Minor, or luce, light--designating Apollo as the god of day.
Aristotle taught in the Lyceum for twelve years (from 335 B.C. until 323 B.C.). It is said that in the mornings he would lecture to his students on logic and metaphysics (the esoteria), and that in the afternoons he would present public lectures on rhetoric, politics, and ethics (the exoteria). Aristotle was succeeded as head of the Lyceum first by Theophrastus and later by Strato.
The proper noun, Lyceum, reappears periodically in the development of Western culture, denoting, for example, the gymnasium/library in Cicero's Tusculan villa, and the English Opera House built, in London, in 1794. In European usage, the common noun, lyceum, and its derivatives typically refers to a school; in American usage, it typically denotes either a hall in which public lectures, concerts, exhibits, etc. are held, or the organization sponsoring such presentations.
-- Indra Rombbo, Locus Nullus Nisi In Tempore