Online Etymology Dictionary

red ink (n.): "financial losses," 1929, from the red ink traditionally used to indicate debits in accounts.
red tape (n.): "excessive bureaucratic rigmarole," 1736, in reference to the red tape formerly used in Great Britain (and the American colonies) for binding up legal and other official documents.
red-eye (n.): "airplane flight which deprives travelers of sleep," 1968, from the red eyes of sleeplessness; earlier as a noun meaning "raw and inferior whiskey" (1819, American English).
red-handed (adj.): 1819, earlier red-hand (early 15c.), originally in Scottish legal writing, from red (1) + hand (n.), presumably from the image of a murderer caught in the act, with blood on the hands.
red-hot (adj.): late 14c., "heated till it glows red" (of metal, etc.); of persons, "lively, passionate," it is recorded from c.1600. Red-hot mama is 1926, jazz slang, "earthy female singer," also "girlfriend, lover."
redact (v.): early 15c., from Latin redact-, past participle stem of redigere "to bring back, collect, reduce," from re- "back, again" (see re-) + agere "to drive" (see act (n.)).
redcap (n.): "porter at a railroad station," 1914, American English, from red (1) + cap (n.).
redcoat (n.): "British soldier," 1510s, from red (1) + coat (n.). Especially of Cromwellian troops in the English Civil War.
redd (v.): early 15c., "to clear" (a space, etc.), from Old English hreddan "to save, to deliver, recover, rescue," from Proto-Germanic *hradjan. Sense evolution tended to merge with unrelated rid. Also possibly influenced by Old English rædan "to arrange," related to Old English geræde, source of ready.

A dialect word in Scotland and northern England, where it has had senses of "to fix" (boundaries), "to comb" (hair), "to separate" (combatants), "to settle" (a quarrel). The exception to the limited use is the meaning "to put in order, to make neat or trim" (1718), especially in redd up, which is in general use in England and the U.S. Use of the same phrase, in the same sense, in Pennsylvania Dutch may be from cognate Low German and Dutch redden, obviously connected historically to the English word, "but the origin and relationship of the forms is not clear" [OED].
redden (v.): 1610s, from red (1) + -en (1). Related: Reddened; reddening.
reddish (adj.): late 14c., from red (1) + -ish. Related: Reddishness.
rede (n.): "counsel, advice," Old English, see read.
redeem (v.): early 15c., from Middle French redemer (see redemption). Related: Redeemed; redeeming.
redeemable (adj.): 1610s, from redeem + -able.
redeemer (n.): mid-15c., agent noun from redeem. In the Christian sense, replaced earlier redemptor.
redefine (v.): 1848, from re- + define. Related: Redefined; redefining; redefinition.
redemption (n.): mid-14c., "deliverance from sin," from Latin redemptionem (nominative redemptio) "a buying back, releasing, ransoming," noun of action from past participle stem of redimere "to redeem, buy back," from re- "back" (see re-) + emere "to take, buy, gain, procure" (see exempt). The -d- is from the Old Latin habit of using red- as the form of re- before vowels, and this is practically the sole English word in which it survives. Redemptorist is from Congregation of the Most Holy Redeemer (founded Naples, 1732, by St. Alphonsus Liguori). In the Mercian hymns, Latin redemptionem is glossed by Old English alesnisse.
redemptive (adj.): 1640s, from redempt (mid-15c., past participle adjective from Latin redemptus, past participle of redimere; see redemption) + -ive.
redeployment (n.): 1945, from re- + deployment.
redesign (v.): 1843, from re- + design (n.). Related: Redesigned; redesigning.
redesign (n.): 1881, probably from redesign (v.).
redhead (n.): mid-13c., from red (1) + head (n.).
The Carrot pate be sure you hate, for she'l be true to no man,
But put her too 't and she will do 't, and oft turns very common:
She that is red upon the head will doubtless ne'r forsake it,
But wanton be, assuredly, and willingly will take it.
["The True Lover's Admonition," Roxburghe Ballads, c.1680]
redirect (v.): 1805 (implied in redirected), from re- "back, again" + direct (v.). Related: Redirecting.
redistribute (v.): 1610s, from re- "back, again" + distribute. Related: Redistributed; redistributing.
redistrict (v.): "redraw the boundaries of districts," 1850, in U.S. political sense, from re- "again" + district. Related: Redistricted; redistricting.
redline (v.): "deny loans to certain neighborhoods based on ethnicity," 1973, on notion of lines drawn on maps. Used earlier in reference to insurance company practices (1961) and in World War II military slang in reference to a red line drawn through a soldier's name for some infraction, thus denying his pay.
redneck (n.): "cracker," 1893; attested 1830 in more specialized sense ("This may be ascribed to the Red Necks, a name bestowed upon the Presbyterians in Fayetteville," from Ann Royall, "Southern Tour I," p.148). According to various theories, red perhaps from anger, or from pellagra, but most likely from mule farmers' outdoors labor in the sun, wearing a shirt and straw hat, with the neck exposed.
redo (v.): also re-do, 1590s, from re- "back, again" + do. Related: Redoing; redone.
redolent (adj.): c.1400, from Old French redolent "emitting an odor," from Latin redolentem, present participle of redolere "emit a scent," from re-, intensive prefix, + olere "give off a smell" (see odor).
redouble (v.): mid-15c., from Middle French redoubler, from Old French re- "again" (see re-) + doubler (see double). Related: Redoubled; redoubling.
redoubt (n.): c.1600, from French redoute, from Italian ridotto "place of retreat," from Medieval Latin reductus "place of refuge, retreat," from Latin reduct-, past participle stem of reducere "to lead or bring back" (see reduce). The -b- was added by influence of unrelated English doubt.
redoubtable (adj.): late 14c., from Old French redoutable (12c.), from redouter "to dread," from re-, intensive prefix, + douter "be afraid of" (see doubt).
redound (v.): late 14c., "to overflow," from Old French redonder "overflow, abound" (12c.), from Latin redundare "to overflow" (see redundant). Meaning "to flow or go back" (to a place or person) is from late 14c.; hence "to rebound" (c.1500), and "to contribute to" (the credit, honor, etc.), c.1500. Related: Redounded; redounding.
redox: 1928, from red(uction) + ox(idation).
redress (v.): mid-14c., from Old French redrecier, from re- "again" (see re-) + drecier "to straighten, arrange" (see dress (v.)). Formerly used in many more senses than currently. Related: Redressed; redressing.
redressal (n.): 1800; see redress + -al (2).
redshirt (v.): "to withdraw (a player) from the varsity team to add a year to his or her eligibility," 1955, in reference to the red shirts worn by athletes on the scrimmage squad.
redskin (n.): "American Indian," 1690s, from red (1) + skin (n.). Red as the skin color of Native Americans is from 1580s; red man is from 1580s.
reduce (v.): late 14c., "bring back," from Old French reducer (14c.), from Latin reducere, from re- "back" (see re-) + ducere "bring, lead" (see duke (n.)). Sense of "to lower, diminish, lessen" is from 1787. Etymological sense preserved in military reduce to ranks (1640s). Related: Reduced; reducing.
reducible (adj.): mid-15c.; see reduce + -ible.
reductio ad absurdum: Latin, literally "reduction to the absurd."
reduction (n.): early 15c., "a restoring to a former state; a subjugation (of a people, etc.)," from Old French reducion (13c., Modern French réduction) and directly from Latin reductionem (nominative reductio), noun of action from past participle stem of reducere (see reduce).
reductionism (n.): 1948, in philosophy, from reduction + -ism. Related: Reductionist.
reductionist (n.): 1861, from reduction + -ist.
reductive (adj.): 1650s, from Medieval Latin reductivus, from reducere (see reduce).
redundance (n.): 1610s, from Latin redundantia, from redundare (see redundant).
redundancy (n.): c.1600; see redundant + -ancy. Sense in employment is from 1931.
redundant (adj.): 1590s, from Latin redundantem (nominative redundans), present participle of redundare "come back, contribute," literally "overflow," from re- "again" (see re-) + undare "rise in waves," from unda "a wave" (see water).
reduplicate (v.): 1560s, from Medieval Latin reduplicatus, past participle of reduplicare "to redouble," from re- "back, again" (see re-) + Latin duplicare "to double" (see duplicate). Related: Reduplicated; reduplicating.
redux: "restored, brought back," Latin, from reducere (see reduce). In book titles at least since 1662 (Dryden, "Astraea Redux").