Ability and possibility (-ebilmek / -abilmek)
Turkish wraps 'can / be able to' into the verb itself. To say I can do, you build yapabilmek (literally 'do-being-able'): stem + -e / -a + bilmek (to know). The result is one long word that you then conjugate normally. Yapabilirim = I can do (it). Türkçe konuşabiliyorum = I can speak Turkish (right now / these days). The negative is irregular and shorter — yapamam = I can't do (it). One construction, three flavors of meaning: ability, permission, possibility.
How to form it — stem + -e/-a + bilmek
Take the verb stem. Add -e or -a by two-way harmony (front vowels e/i/ö/ü → -e; back vowels a/ı/o/u → -a). Then attach bilmek ('to know') as a helper verb. yap- + -a- + bilmek = yapabilmek (to be able to do). gel- + -e- + bilmek = gelebilmek (to be able to come). konuş- + -a- + bilmek = konuşabilmek (to be able to speak). If the stem ends in a vowel, you need a buffer -y-: oku- + -y- + -a- + bilmek = okuyabilmek.
Conjugating the result
Once you have the -ebilmek/-abilmek infinitive, conjugate it like any verb. Aorist for general ability: yapabilirim = I can do (in general). Continuous for current ability or right-now possibility: yapabiliyorum = I'm able to do / I can do (these days). Past: yapabildim = I was able to do. Future: yapabileceğim = I'll be able to do. The aorist form is the most common — Turkish 'I can swim' is Yüzebilirim, not 'yüzebiliyorum'.
The negative is different — -ama / -eme
Crucially, the negative of 'can' is not 'yapabilmemek'. Turkish uses a separate negative ability marker: -ama / -eme (back / front harmony) inserted between stem and the personal endings, without bilmek. yap- + -ama- = yapama-, then conjugated: yapamam (I can't), yapamazsın (you can't), yapamaz (he can't), yapamayız (we can't), yapamazsınız, yapamazlar. Notice the aorist endings are the negative aorist set from lesson 20 (-mam / -mazsın / -maz / -mayız / -mazsınız / -mazlar). For other tenses: continuous yapamıyorum = I can't (right now); past yapamadım = I couldn't; future yapamayacağım = I won't be able to.
Use 1: ability
Knowing how to do something. Türkçe konuşabilirim = I can speak Turkish. Yüzebiliyor musun? = can you swim? Bu kelimeyi okuyamıyorum = I can't read this word. The aorist tends to mean 'I can in general' (skill); the continuous tends to mean 'I'm able to right now' (current circumstance). Araba kullanabilirim = I can drive (I have the skill). Bugün araba kullanamıyorum = I can't drive today (something is preventing me).
Use 2: permission
Can I…? for asking and giving permission. Buraya oturabilir miyim? = can I sit here? (asking permission). Tabii ki gidebilirsin = of course you can go. Bu odaya giremezsiniz = you can't enter this room (negative — both ability and permission readings are possible; context decides). For polite requests, the aorist + question is the standard form: Yardım edebilir misiniz? = could you help (me)?
Use 3: possibility
It might / could happen. Third-person aorist plus -ebilir/-abilir marks possibility, often with belki (maybe). Yarın yağmur yağabilir = it might rain tomorrow. O gelmeyebilir = he might not come (note the negative goes before -ebilmek, not the -ama negative — because we mean 'it's possible he won't come', not 'he's unable to come'). Belki haklı olabilir = maybe she's right. Olabilir alone = 'it's possible / could be'.
Two negatives, two meanings
Subtle but important: gelmeyebilir vs gelemez. gelmeyebilir = he might not come (possibility of not coming); built as stem + -me (verb negative) + -y- + -ebil- + person ending. gelemez = he can't come (inability); built with the special -eme marker. The two are not interchangeable: Yarın yağmayabilir = it might not rain (real possibility); Yağmur yağamaz would mean 'rain is incapable of falling', which is nonsense. Pick by meaning.
