"-(으)ㄹ 래요 / -겠어요 / -(으)ㄹ 께요 / - (으)ㄹ 거예요" => -(으)ㄹ래요 / -겠어요 / -(으)ㄹ게요 / -(으)ㄹ 거예요. Here's some more information and examples using the casual versions -ㄹ래, -겠어, -ㄹ게, and -ㄹ 거야. -ㄹ래: shows one's desire or intention rather directly. Sounds very informal (and sometimes willful). -곘어: 1. equivalent to -ㄹ래 in meaning, but is more formal. -곘어: 2. expresses a likely or expected event or condition (often as a consequence of something). -ㄹ게: shows one's intention while taking care to let the other person know, as it might affect him/her. -ㄹ 거야: 1. same as -ㄹ래 or -겠어, 2. declares or predicts future event without involving one's will (future tense). So most of them (except -겠다 #2 and -ㄹ 거야 #2) are about one's intention rather than a future event. Future tense is expressed using -ㄹ 것이다 or other less used literary forms like -리라 and -리. Examples: - 이 책 읽어 볼래?: Would you like to read this book? - 난 그런 짓은 하지 않겠어 (#1): I won't do such a thing. - 저 차 저렇게 빨리 달리다가 사고 나겠다 (#2): I'm afraid that car might cause an accident driving so fast. - 나는 볼일이 있어서 먼저 갈게: I'll take off first because I have some business to take care of. - 나는 열심히 공부해서 성공할 거야 (#1): I will study hard and succeed. - 우리 집은 내년에 인천으로 이사할 거야 (#2): Our family will [is going to] move to Incheon next year.

I'm not a native speaker, but I'll try to answer your questions! -(으)ㄹ래요. I tend to think of this as "Shall we/I ___?" It could also mean "Do you want to __?". I think this grammar point is used more in a question form, not declarative, but it's still used both ways: 나: 우리는 뭐 먹을래? (What shall we eat?) 가: 흠...김밥요? (Hm...kimbap?) 나: 지금 뭐 해요? (What are you doing now?) 가: 늦어서 이제 잘래. (It's late so I shall/will go to sleep.) -겠어요. This is just the basic way of saying something in the future. Like: 하겠어. However -겠어요 is usually used when you're using the high honorific form or when you say something seems like it would be good/fun/etc. 가: 네, 잘 먹겠습니다. (Yes, I'll eat good.) 나: 와~그 밥은 진짜 맛있겠다! (Wow, that food looks so good!) -(으)ㄹ 께요. I think you mean ~(으)ㄹ게요. Sometimes it's written like that, since it's said like that.This is another future tense form however, this has a slight nuance that you're asking someone if it's okay. 나: (널 위해) 문을 열을게. (I'll open the door [for you] 'if that's okay'.) 가: (당신을 위해) 밥을 살게. (I'll buy food [for you] 'if that's okay with you'.) 다: 잘게. (I'm going to sleep now 'if that's okay'.) - (으)ㄹ 거예요. Unlike ~(으)ㄹ게요, - (으)ㄹ 거예요 means you ARE going to do it, without the person's "permission". However remember it's just a slight nuance though, they can be interchangeable. 나: 내일 학교에 갈 거야. (I'm going to school tomorrow.) 가: 엉덩이 아파서 앉을 거예요. (My butt hurts so I'm going to sit down.) I hope I answered your questions! ^^ If you have any questions, just ask~