prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").
The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.
It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.
early 15c., redemen, "buy back, ransom, recover by purchase," also in a theological sense, "deliver from sin and spiritual death," from Old French redimer "buy back" and directly from Latin redimere "to redeem, buy back," from red- "back" (see re-) + emere "to take, buy, gain, procure" (from PIE root *em- "to take, distribute").
In Middle English, Latin redimere sometimes was translated as againbuy. The general sense of "rescue, deliver, save" is from late 15c. The meaning "make amends for" is from 1520s. Sense of "make good, perform, fulfill" (a promise, obligation, etc.) is from 1840. The commercial sense of "receive back by paying the obligation" is by 1889. The sense of "save (time) from being lost" (Tindale, Shakespeare, Young, Cowper, Eliot) is after Ephesians v.16, Colossians iv.5. Related: Redeemed; redeeming; redempt (obsolete).