But take heart!
You're not studying Old Irish!
Some quotes from Fortston's Indo-European Language and Culture (for the Unicode un-enabled, I use a circumflex for the macron):
14.45. As these examples hint at, the effects of syncope [loss of sounds in the interior of a word, annis] and apocope [removal of final syllables, annis] in Irish are nowhere as apparent or as devastating as in verbal conjugations, especially those of verbs compounded with one or more preverbs. The effects are particularly widespread partly due to the fact that Old Irish had an especial fondness for piling preverbs together, giving syncope and apocope no shortage of syllablic gallows-fodder. ...
14.46. The amount of allomorphy (that is, variation in the form of a given morpheme) that these changes created was incredible, and it is worth digressing to give some examples. The Irish root fêd- 'say' appears in such varied guises as fét, id and d, as in the following forms of the compound verb *at-fêd- 'relate': 3rd sing. present ad-fét 'relates', perfective present ad-cuïd (*ad-com-fêd), and 2nd pl. conjunct perfective present -éicdid. Sometimes the root is reduced to a single sound, particularly in the conjunct 3rd person singular s-subjunctive. Thus the 3rd sing. conjunct s-subjunctive of the verb as-boind (*as-bond-) 'refuses' is simply -op (pronounced -ob, the regular outcome of *-óss-bod-s-t!); and from *ret- 'run' (present rethid 'runs') we have the compound do-fúarat 'remains over' (*di-fó-uss-ret-), whose conjunct 3rd sing. s-subjunctive is -diúair (< [i]*dí-fo-uss-ret-s-t), with only the -r remaining of the original root, subjunctive suffix and personal ending (and very little left of the preceding preverbs).
Latin and Greek are a snap compared to these amazing evaporating verbs.