Old English or Anglo-Saxon (c. 500-1200 C.E.): It's a language, not a description of old writing.
Non-English-majors commonly call any archaic dialect of English "Old English," or more properly "old English." They usually are talking about Shakespeare's Early Modern English, or Chaucer's Middle English. Specialists also know of a language that is more properly called Old English, or the language of the Anglo-Saxon tribes, a tongue spoken in four major dialects (West Saxon, Mercian, Northumbrian, and Kentish) during a period between roughly 500 and 1200 C.E.. The language began as the tongue of invading Germanic tribes who drove back the Celts, Picts, and other previous invaders of the island toward the borderlands to the north (now Scotland), south (now Cornwall), and west (now Wales, and Ireland). Not surprisingly, for this reason, Old English sounds like German. Some Celtic words survived in place names ("Baltimore," in West Cork, Ireland = Baal-ti-Moor, or "the high place of Baal [a god]"), and in the surviving languages of Gaelic and Welsh. Some of the Celts also fled to Ireland and back across the English Channel (AKA la Manche) into what is now Brittany, sometimes called "Little Britain" in Arthurian Romance. The Angles and Saxons moved the furthest inland, and the Jutes tended to settle on the eastern Channel coast in what is now Kent. Kentish dialect still preserves distinctive differences because of residual Jutish usages. The linguistic mixture of Old English also absorbed Norse words from resident Viking communities in the northwest, and Danish words from the eastern kingdom ruled under the "Danelaw." The language of literate English people was Latin, and Latin, too, contributed many words to Old English and its successor, Middle English. The shift from Old to Middle English may have taken two or more generations, but its most obvious cause was the 1066 C.E. invasion of England by a Norman French speaking army under the command of William of Normandy, AKA "William the Bastard." Norman French became the language of government, law, and polite literature, and Old English was relegated to the peasants' fields and isolated Anglo-Saxon households holding out for a return of the old regime that never came. Spoken proficiency in Old English was far more common than Old English literacy, and this dramatically reduced the survival rate of poems, chronicles, and other works in the tongue spoken by the Anglo-Saxons. Meanwhile, the sound and grammar of Old English continued to collide with that of Norman French over the next one to two hundred years until a hybrid language we know as Middle English became commonly used, first for ordinary commerce and then, slowly, for works of literature.