I-mutation has occurred in many languages (for example, it explains the alternations between Portuguese fiz < */fetsi/ "I did" vs. fez < */fetse/ "he did"). However, the term is usually taken (especially when referred to using the name "i-umlaut") to processes in the early Germanic languages.
I-mutation is usually used to refer to a particular set of changes in the old Germanic languages. I-mutation is particularly important because it was productive in the prehistory of the Germanic languages and led to many alternations that are visible in the morphology of these languages, due to the prevalence of inflectional suffixes containing an /i/ or /j/.
This process took place separately in the various Germanic languages starting around 450 or 500 AD in the North Sea area, and affected all of the early languages except for Gothic. It seems to have taken effect earliest, and was most complete in its implementation, in Old English and Old Norse. It took place later in Old High German, and by 900 AD its effects were visible only on /a/. (However, it is argued that /o/ and /u/ were already affected allophonically.)
The word "umlaut" can have other meanings. See Umlaut.
I-mutation affects vowels as follows:
The situation in Old Norse is complicated as there are two forms of i-mutation. Of these two, only one is phonologized. I-mutation in Old Norse is phonological if:
I-mutation is not phonological if the vowel of a long syllable is i-mutated by a syncopated i. I-mutation does not occur in short syllables.
|a||e (ę)||fagr (fair) / fegrstr (fairest)|
|au||ey||lauss (loose) / leysa (to loosen)|
|á||æ||Áss (god) / Ǣsir (gods)|
|jú||ý||ljúga (to lie) / lýgr (lies)|
|o||ø||koma (to come) / kømr (comes)|
|ó||œ||róa (to row) / rœr (rows)|
|u||y||upp (up) / yppa (to lift up)|
|ú||ý||fúll (foul) / fýla (stink, foulness)|
|ǫ||ø||sǫkk (sank) / søkkva (to sink)|
I-mutation is visible in Old High German (OHG), c. 800 AD, only on /a/, which was mutated to /e/. By this point, it had already become partly phonologized, since some of the conditioning /i/'s and /j/'s had been deleted or modified. The later history of German, however, shows that /o/ and /u/ were also affected, -- starting in Middle High German, the remaining conditioning environments disappear and /o/ and /u/ appear as /ø/ and /y/ in the appropriate environments.
This has led to a controversy -- when and how did i-mutation appear on these vowels? Some have suggested that the vowels must have been modified already in OHG, but was not indicated due to the lack of proper symbols, and/or because they were still partly allophonic. Others have suggested that the i-mutation of /o/ and /u/ was entirely analogical, and pointed to the lack of i-mutation of these vowels in certain places where it would be expected, in contrast to the consistent mutation of /a/. Perhaps the answer is somewhere in between -- i-mutation of /o/ and /u/ was indeed phonetic, occurring late in OHG, but later spread analogically to the environments where the conditioning had already disappeared by OHG (this is where failure of i-mutation is most likely).