resolve v.

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state;" "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]

1580s, "form of speech peculiar to a people or place;" meaning "phrase or expression peculiar to a language" is from 1620s; from French idiome (16c.) and directly from Late Latin idioma "a peculiarity in language," from Greek idioma "peculiarity, peculiar phraseology" (Fowler writes that "A manifestation of the peculiar" is "the closest possible translation of the Greek word"), from idioumai "to appropriate to oneself," from idios "personal, private," properly "particular to oneself."

This is from PIE *swed-yo-, suffixed form of root *s(w)e-, pronoun of the third person and reflexive (referring back to the subject of a sentence), also used in forms denoting the speaker's social group, "(we our-)selves" (source also of Sanskrit svah, Avestan hva-, Old Persian huva "one's own," khva-data "lord," literally "created from oneself;" Greek hos "he, she, it;" Latin suescere "to accustom, get accustomed," sodalis "companion;" Old Church Slavonic svoji "his, her, its," svojaku "relative, kinsman;" Gothic swes "one's own;" Old Norse sik "oneself;" German Sein; Old Irish fein "self, himself").

[G]rammar & idiom are independent categories; being applicable to the same material, they sometimes agree & sometimes disagree about particular specimens of it; the most can be said is that what is idiomatic is far more often grammatical than ungrammatical, but that is worth saying, because grammar & idiom are sometimes treated as incompatibles .... [Fowler]