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investigación f. (Noun) "investigation"
From Latin investigationem, accusative of investigatio 'id.' From the verb investigare "to investigate" (see investigar).
Indo-European
Romance
Italian investigazione
investigar (Verb) "to investigate"
From Latin investigare 'id.' From in- "in" (see in- (2)) and vestigare "to follow a track;" from vestigium "track" (see vestigio).
Indo-European
Romance
French investiguer
invierno m. (Noun) winter
14th cent. Earlier 12th cent. Old Spanish ivierno. From Late Latin hibernum "winter" (descending from the Latin tempus hibernum "winter season"). From Proto-Italic *χeim-r-ino- (adj.) "winter," from Proto-Italic *χeim- "winter" (whence hiemal).
Indo-European
Romance
Portuguese inverno, Galician inverno, Catalan hivern, French hiver, Italian inverno, Aromanian earnã, Romanian iarnă, Sardinian jerru
inyectable (Adjective) "injectable"
From inyectar.
inyectar (Verb) "to inject"
From Latin iniectare 'id.,' a frequentive from inicere "to throw in." Composed of in- (2) and iacere "to throw" (see echar).
-ío Noun-forming suffix to form abstract nouns from verbs.
From Latin -io, originally an -o suffix on i-stem verbs.
ir (Verb) "to go"
11th cent. This modern Spanish verb, infamously irregular, is a collapse of multiple Latin verbs into a single word. Penny (2002) explains why the old Latin forms of this verb were replaced by forms from other verbs: "The present-tense forms [in Latin] suffered from the disadvantage of having no consonant in the root. ...This fact must have made these forms difficult to separate from adjacent words in normal speech, and which caused the majority of them to be replaced by longer forms, drawn from other verbs."

Forms beginning with i- (ir, iba, etc…) derive from Latin ire 'id.' (see below). Latin ire is from Proto-Italic *ei- "to go." From Proto-Indo-European *h1ei̯- 'id.'
Forms with v- (voy, vaya, etc…) were taken from vadere "to go," "to walk" (see voy).

Forms beginning with f- (fui, fueras, etc...) were borrowed from ser (see fui and ser).
-ísimo Superlative suffix.
From Latin -issimus 'id.' From Proto-Italic *-ism̥mo- 'id.' with a post-Proto-Italic expressive lengthening of the -s- to -ss-. A compound of *-is-, a comparative suffix, and *-(t)m̥mo-. For the origin of *-(t)m̥mo-, see -tr-. Proto-Italic *-i̯s- is from Proto-Indo-European *-i̯s-to-, the original superlative suffix in Proto-Indo-European.
Indo-European
Romance
Portuguese -íssimo, Catalan -íssim, French -issime, Italian -issimo
Italic
Paelignian -ismu (< Proto-Italic *-isamo), Oscan -imas (pre-form *-ismo-), Umbrian -ime (pre-form *-ismo-)
Celtic
Old Irish -(i)ssam, Middle Welsh -af, Breton -aff, Celtiberian (f.) -sama, Gaulish (f.) -xama
"Now, 'expressive' [lengthening] has been invoked frivolously over the years, and is little more than a gong announcing the lack of a real explanation. But in this case for once it is not far-fetched. The superlative adjective has a distinct, and salient, semantic 'push', an emphasis which is often moreover conscious, like the emphatic aspirated stops in French in place of the otherwise plain articulation of such consonants. Besides, one might suppose that the prosodics of the specific form pessimus 'worst'... would inevitably contribute to the ultimate success of the ending -(i)ssimus." ~ A. Sihler, New Comparative Grammar of Greek and Latin (2008)
isla f. (Noun) "island"
13th cent. From Latin insula 'id.' Of unknown origin. Presumably borrowed from a non-Indo-European language.
As for the origin of the surnames de la Isla, Islas, Islán, and Isoler, they originally indicated that the individual hailed from the town of Isla, Cantabria.
Indo-European
Romance
Asturian isla, Portuguese isla, Galician insua, Catalan illa, French île, Italian isola, Romanian insulă, Sardinian isula
-ismo Suffix forming abstract nouns from verbs.
Borrowed from Greek -ισμός (-ismós) 'id.' Rebracketing of the the verb-forming suffix -ῐ́ζ- (-idz-) and the older noun-forming suffix -μός (-mós).

Suffix -ῐ́ζ- is from the verbal suffix *-idi̯eti in Proto-Indo-European. From *-id- and the *-i̯eti, a suffix that turned transitive verbs into intransitive imperfective verbs.

Suffix *-i̯eti became the -io-stem in Latin, appearing in third and fourth conjugation verbs (e.g., Latin capio "I capture" ); and, for the most part, has not survived in any obvious way in Spanish. Latin -io has been leveled to -o (capio is now cabo), conforming with other Spanish first-person singular endings.

The noun-forming suffix -μός is from Proto-Indo-European *-mo-s (whence -mo).