Etymology
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guest (n.)
Old English gæst, giest (Anglian gest) "an accidental guest, a chance comer, a stranger," from Proto-Germanic *gastiz (source also of Old Frisian jest, Dutch gast, German Gast, Gothic gasts "guest," originally "stranger"), from PIE root *ghos-ti- "stranger, guest, host" (source also of Latin hostis, in earlier use "a stranger," in classical use "an enemy"); the root sense, according to Watkins, probably is "someone with whom one has reciprocal duties of hospitality."

Spelling evolution influenced by Old Norse cognate gestr (the usual sound changes from the Old English word would have yielded Modern English *yest). Meaning "person entertained for pay" (at an inn, etc.) is from late 13c. Old English also had cuma "stranger, guest," literally "a comer." Phrase be my guest in the sense of "go right ahead" first recorded 1955.
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guest (v.)
early 14c., "receive as a guest;" 1610s, "be a guest;" 1936, American English, "appear as a guest performer," from guest (n.). Related: Guested; guesting.
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guest-room (n.)
also guestroom, 1630s, from guest (n.) + room (n.). Guest chamber is recorded from 1520s. Old English had giestærn "guest-chamber," with the second element the same one as in barn.
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guest star (n.)
1914 in the entertainment sense; earlier the phrase was used literally, of novae. As a verb, by 1942.
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*ghos-ti- 

Proto-Indo-European root meaning "stranger, guest, host," properly "someone with whom one has reciprocal duties of hospitality," representing "a mutual exchange relationship highly important to ancient Indo-European society" [Watkins]. But as strangers are potential enemies as well as guests, the word has a forked path.

The word ghos-ti- was thus the central expression of the guest-host relationship, a mutual exchange relationship highly important to ancient Indo-European society. A guest-friendship was a bond of trust between two people that was accompanied by ritualized gift-giving and created an obligation of mutual hospitality and friendship that, once established, could continue in perpetuity and be renewed years later by the same parties or their descendants. [Calvert Watkins, "American Heritage Dictionary of Indo-European Roots"]

It forms all or part of: Euxine; guest; hospice; hospitable; hospital; hospitality; hospodar; host (n.1) "person who receives guests;" host (n.2) "multitude;" hostage; hostel; hostile; hostility; hostler; hotel; Xenia; xeno-; xenon.

It is the hypothetical source of/evidence for its existence is provided by: Greek xenos "guest, host, stranger;" Latin hostis, in earlier use "a stranger," in classical use "an enemy," hospes "host;" Old Church Slavonic gosti "guest, friend," gospodi "lord, master;" Old English gæst, "chance comer, a stranger."

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Xenia 
city in Ohio, from Greek xenia "hospitality, rights of a guest, friendly relation with strangers," literally "state of a guest," from xenos "guest" (from PIE root *ghos-ti- "stranger, guest, host"). Founded 1803 and named by vote of a town meeting, on suggestion of the Rev. Robert Armstrong to imply friendliness and hospitality.
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xeno- 
before vowels, xen-, word-forming element meaning "strange, foreign; stranger, foreigner," from Greek xenos "a guest, stranger, foreigner, refugee, guest-friend, one entitled to hospitality," cognate with Latin hostis, from PIE root *ghos-ti- "stranger, guest, host." "The term was politely used of any one whose name was unknown" [Liddell & Scott].
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convival (adj.)

1640s, from Latin convivalis "pertaining to a feast or guest," from conviva "a feaster, guest," from convivere (see convivial). It has been replaced in most uses by convivial, which means the same.

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hospital (n.)

mid-13c., "shelter for the needy," from Old French hospital, ospital "hostel, shelter, lodging" (Modern French hôpital), from Late Latin hospitale "guest-house, inn," noun use of neuter of Latin adjective hospitalis "of a guest or host" (as a noun, "a guest; the duties of hospitality"), from hospes (genitive hospitis) "guest; host;" see host (n.1).

The sense of "charitable institution to house and maintain the needy" in English is from early 15c.; the meaning "institution for sick or wounded people" is recorded by 1540s. The same word, contracted, is hostel and hotel. The sense shift in Latin from duties to buildings might have been via the common term cubiculum hospitalis "guest-chamber." The Latin adjective use continued in Old French, where ospital also could mean "hospitable" and ospitalite could mean "hospital."

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host (n.1)

"person who receives guests," especially for pay, late 13c., from Old French oste, hoste "guest, host, hostess, landlord" (12c., Modern French hôte), from Latin hospitem (nominative hospes) "guest, stranger, sojourner, visitor (hence also 'foreigner')," also "host; one bound by ties of hospitality."

This appears to be from PIE *ghos-pot-, a compound meaning "guest-master" (compare Old Church Slavonic gospodi "lord, master," literally "lord of strangers"), from the roots *ghos-ti- "stranger, guest, host" and *poti- "powerful; lord." The etymological notion is of someone "with whom one has reciprocal duties of hospitality" [Watkins]. The biological sense of "animal or plant having a parasite" is from 1857.

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