Want & Can: ~고 싶다, ~(으)ㄹ 수 있다
Express what you want to do and what you are able to do.
Expressing desire and ability in Korean unlocks a huge range of natural conversation. -고 싶다 attaches to a verb stem to mean 'want to': 가다 (go) → 가고 싶다 (want to go) → 가고 싶어요 (polite: I want to go). The pattern is identical for any verb.
-(으)ㄹ 수 있다 / 없다 expresses ability: 하다 → 할 수 있어요 (I can do it) / 할 수 없어요 (I cannot do it). The (으) appears after consonant-ending stems for euphony. The phrase 수 있다 literally means 'there is a way', which is a natural way to express possibility in Korean. Note the contrast with 못 from Lesson 3-4: -(으)ㄹ 수 없다 is a softer way of saying 'cannot', while 못 is more direct. In conversation, Koreans often soften refusals using 못 하겠어요 or 못 할 것 같아요 instead of a flat 안 해요, which can sound rude.
~고 싶다 — Want to do
Attach 고 싶다 to the verb stem (remove 다). 가다 → 가고 싶어요 (I want to go). For past: 고 싶었어요 (I wanted to).
~(으)ㄹ 수 있다/없다 — Can / Cannot
Verb stem + (으)ㄹ 수 있다 = can do. If stem ends in consonant → 을 수 있다, vowel → ㄹ 수 있다. Replace 있다 with 없다 for 'cannot'.