Online Etymology Dictionary

understate (v.): 1824, from under + state (v.). Related: Understated (of fashions, etc., from 1957); understating.
understatement (n.): 1799, from under + statement. Understated, with reference to clothing, is recorded from 1957.
understory (n.): in reference to forest vegetation, also under-story, 1902, from under + story (n.).
understudy (v.): also under-study, 1852, in the theatrical sense, from under + study (v.). The noun is attested from 1848, translating Italian supplimento.
undertake (v.): c.1200, "to entrap," in the same sense as Old English underniman (cf. Dutch ondernemen, German unternehmen), of which it is a partial loan-translation, from under + take. Cf. also French entreprendre "to undertake," from entre "between, among" + prendre "to take." The under in this word may be the same one that also may form the first element of understand. Meaning "to accept" is attested from mid-13c.; that of "to take upon oneself, to accept the duty of" is from c.1300.
undertaker (n.): c.1400, "a contractor or projector of any sort," agent noun from undertake (v.). The specialized sense (1690s) emerged from funeral-undertaker.
undertaking (n.): "enterprise," early 15c., verbal noun from undertake (v.).
undertone (n.): 1762, "low or subdued tone," from under + tone. Figurative sense of "undercurrent of feelings, etc.," is attested from 1861.
undertow (n.): 1798, from under + tow (n.).
underutilize (v.): also under-utilize, 1949, from under + utilize. Related: Underutilized; underutilizing.
undervalue (v.): 1590s, "to rate as inferior in value" (to), from under + value (v.). Sense of "to estimate or esteem too low" is recorded from 1610s. Meaning "to rate at too low a monetary value" is attested from 1620s.
underwater (adj.): 1620s, from under + water (n.). Of mortgages from 2008.
underway (adv.): 1749, of ships, "having begun to move," from under + way. In reference to projects, activities, etc., it is attested from 1935.
underwear (n.): 1872, from under + wear (n.). So called because it is worn under one's clothing.
underweight (adj.): 1899, from under- + weight.
underwhelm (v.): 1953 (implied in underwhelming), a facetious play on overwhelm. Related: Underwhelmed; underwhelmingly.
underworld (n.): c.1600, "the lower world, Hades," also "the earth," as distinguished from heaven. Cf. German unterwelt, Dutch onderwereld, Danish underverden. Meaning "lower level of society" is first recorded 1890; "criminals and organized crime collectively" is attested from 1900.
underwrite (v.): early 15c., from under + write (v.). A loan-translation of Latin subscribere (see subscribe). Used literally at first; modern sense of "to accept the risk of insurance" (1620s) is from notion of signing a marine insurance policy. Meaning "to support by a guarantee of money" is recorded from 1890.
underwriter (n.): 1610s, "subscriber;" insurance sense from 1620s; agent noun from underwrite.
undeserved (adj.): late 14c., from un- (1) "not" + past participle of deserve.
undeserving (adj.): 1540s, from un- (1) "not" + present participle of deserve.
undesirable (adj.): 1660s, "not to be desired, objectionable," from un- (1) "not" + desirable. The noun meaning "undesirable person or thing" is first attested 1883. Undesired "not asked or invited" is recorded from late 15c.
undetected (adj.): 1590s, from un- (1) "not" + past participle of detect. Undetectable is recorded from 1863.
undetermined (adj.): mid-15c., from un- (1) "not" + past participle of determine.
undeterred (adj.): c.1600, from un- (1) "not" + past participle of deter.
undeveloped (adj.): 1736, from un- (1) "not" + past participle of develop. In reference to film, it is attested from 1939.
undeviating (adj.): 1732, from un- (1) "not" + present participle of deviate.
undies (n.): 1906, diminutive euphemistic abbreviation for women's underwear (or undergarments).
undifferentiated (adj.): 1862, from un- (1) "not" + past participle of differentiate.
undigested (adj.): 1520s, from un- (1) "not" + past participle of digest (v.). Figurative sense is recorded from c.1600.
undignified (adj.): 1680s, of clergy, "not holding a position of dignity," from un- (1) "not" + dignified. Meaning "lacking in dignity of manner" is attested from 1782.
undiluted (adj.): 1756, from un- (1) "not" + past participle of dilute.
undiminished (adj.): 1580s, from un- (1) "not" + past participle of diminish.
undine (n.): 1821, from Modern Latin Undina (1650s), coined by Paracelsus ("De Nymphis") for a water spirit in his alchemical system, from Latin unda "a wave" (see water). Popularized by German romance "Undine, eine Erzählung" (1811) by Baron F.H.C. La Motte Fouqué. Undinism (1928) was coined by sex researcher Havelock Ellis to describe the fetish for urine (which Ellis had); nowadays it would be called urophilia.
undisciplined (adj.): late 14c., "untrained," from un- (1) "not" + past participle of discipline (v.). Cf. German undisciplinirt, Swedish odisciplinerad. Specific meaning "not subject to military discipline" is attested from 1718.
undisclosed (adj.): 1560s, from un- (1) "not" + past participle of disclose.
undiscovered (adj.): 1540s, from un- (1) "not" + past participle of discover.
undisguised (adj.): c.1500, in reference to things, from un- (1) "not" + past participle of disguise (v.). Of persons, attested from 1670s.
undismayed (adj.): 1610s, from un- (1) "not" + past participle of dismay.
undisputable (adj.): 1590s, from un- (1) "not" + disputable (see dispute). The usual word is indisputable. Related: Undisputably.
undisputed (adj.): 1560s, "not argued with," from un- (1) "not" + past participle of dispute (v.). Meaning "not called into question" is attested from 1620s.
undistinguishable: 1580s, from un- (1) “not” + distinguishable.
undistinguished (adj.): 1590s, "not kept distinct," from un- (1) "not" + distinguished. Meaning "not elevated above others" is attested from 1600.
undisturbed (adj.): c.1600, from un- (1) "not" + past participle of disturb.
undivided (adj.): early 15c., from un- (1) "not" + past participle of divide.
undo (v.): Old English undon "to unfasten and open" (a window or door), "to unfasten by releasing from a fixed position," from un- (2) + do (v.). The notion is of "to annul something that was done." Related: Undone; undoing.
undocumented (adj.): 1883, from un- (1) "not" + past participle of document (v.).
undomesticated (adj.): 1834, from un- (1) "not" + past participle of domesticate. Undomestic "not caring for home life" is recorded from 1754.
undone (adj.): "not accomplished," c.1300, from un- (1) + done. The same word meaning "destroyed" is recorded from mid-14c., past participle adjective from undo.
undoubtable (adj.): early 15c., from un- (1) "not" + doubt + -able.