Alliterative verse is a style of writing that could be used to create poems of many genres. I include it in this list of "forms" because works written in alliterative verse have some characteristic attributes that distinguish their work from the rhyming verse and prose works. They tend to represent older, non-French values associated with the old Anglo-Saxon, pre-Conquest culture. Some scholars think they originated in an "Alliterative Revival" in the Fourteenth Century, perhaps in baronial halls on the North and West marches of England where they expressed a nostalgia for older, less "Continental" aesthetics and values, but other scholars believe the Anglo-Saxon alliterative poetics we saw in Beowulf and "Battle of Maldon" persisted over the intervening three centuries without leaving written records until the Fourteenth Century (see Chism and Cable below). A synthesis of both theses is entirely imaginable, and attempts to historicize the circumstances under which a "privileged manuscript of a nostalgic Anglo-Saxonist poet" might emerge have produced some inventive solutions. For instance, John Bowers has argued that the Pearl-Poet (AKA, Gawain-Poet) flourished at the court of Richard II. We know that the young king, suspicious of the older baronial magnates who persecuted his young friends, hired a troupe of Cheshire archers as his personal bodyguard. Bowers suspects they either hired a local Cheshire poet or one of their number was exceptionally gifted and created these great poems as nostalgic entertainment in their home dialect, comfort amid the very court that oppressed the court cultures of the Marches as marginal outsiders. The dialect of the Pearl-Poet's works bears some debatable similarities with Cheshire dialect and the places referred to in "Sir Gawain and the Green Knight" include Cheshire locations unlikely to appear in an East Midlands poet's work (i.e., from around London). You do not have to be much further acquainted with these theories in order to read alliterative verse, but it helps to know the controversy exists with respect to the values with which this style of composition is associated.
What is alliterative verse? Most Renaissance poetry, other than blank verse, is organized by meter and by rhyme. The meter gives lines their syntactic framework, constraining the number and types of syllables words may be composed of, and the rhyme gives lines their "music," a phonological system of interlocking reference that usually links ends of lines, but sometimes also connects the end rhymes to "internal rhyme" within lines. Medieval alliterative verse is organized by stress, usually four stresses per line. As long as the line contains those four stresses, syllable count within the line can vary considerably. For that reason, alliterative verse is a more forgiving form in which to write, offering poets more kinds of words to choose from in each syntactic situation. The best alliterative poets, however, do not take lazy advantage of that freedom, but rather control their lines with tightly constructed patterns of internal rhyme, consonance, and assonance, that play off the alliteration of the first syllables. Truly extraordinary alliterative poets, like the Pearl-Poet, use alliteration and rhyme and meter simultaneously. The twelve-line concatenated rhyme of "Pearl"'s 101 stanzas, and the "bob-and-wheel" stanzas of "Sir Gawain and the Green Knight," are among the highest formal achievements of English medieval literature.
Interpretation of alliterative verse often uses the same methodologies used by interpretations of any lyric poem. New Criticism's close reading analysis, combined with a variety of other methods like Feminist, Marxist, Psychoanalytic, New Historicist, Structuralist, and Deconstructive interpretation, can provide a wealth of insights from even very short poems. Longer narrative alliterative verse, however, can benefit from Reader-Response criticism even more than the short lyrics.
Some Book-Length Print Resources
Bowers, John M. The Politics of Pearl: Court Poetry in the Age of Richard II. Cambridge: D.S. Brewer, 2001.
Cable, Thomas. The English Alliterative Tradition. Philadelphia: U of Pennsylvania P, 1991. 821.9 C115e
Chism, Christine. Alliterative Revivals. Philadelphia: U of Pennsylvania P, 2002. 821.9 C542a