It indicates the speaker's intention or will, and also used to ask the listener's intention or will in colloquial(semi-casual) communications.
-으ㄹ래요 can only be added to a verb. It is only used for the first person, and the second person subjects. It cannot be used for the third person subject.
-을래요. is added to the stem that ends in a consonant
-ㄹ래요. is added to the stem that ends in a vowel
-래요 is added to the ㄹ irregular verb
저와 같이 음악 들을래요? Will you listen to the music with me?
듣다's stem '듣' ends in a consonant 'ㄷ', so -을래요. is added to the stem.
코믹 영화 볼래요? Will you watch a comic movie?
판타지 영화를 볼래요. (I) will watch a fantasy movie.
The stem of 보다 is 보, which ends in a vowel 'ㅗ'. Therefore -ㄹ래요. is added to the stem.
무슨 과목을 공부할래요? Which subject will you (intend to) study?
수학을 공부할래요. (I) will study math.
공부하다's stem '하' ends in a vowel 'ㅏ'. So -ㄹ래요. is added to the stem.
It indicates the speaker's promise or willingness to do something to the listener's interest, or used when the speaker volunteers to do something. It is only used for the first person and with the verbs. You cannot question with the -으ㄹ게요 ending.
저녁 7시까지 갈게요.
방 청소 할게요.
제가 박스 옮기는 거 도와드릴게요.
제가 공항까지 바래다 드릴게요.
When the subject of the sentence is the speaker, it is used to show a speaker's wondering mind. On the other hand, if a third person is the subject of the sentence, then is is used to seek the opinion of the listener. You can also question the listener alternatively with the repeated use of -(으)ㄹ까요?
-을까요 is added to the stem that ends in a consonant.
e.g.찾다(to find) / 찾+을까요? → 찾을까요?
ㄹ까요 is added to the stem that ends in a vowel.
e.g.도우다(to help) / 도우+ㄹ까요?→ 도울까요?
-까요 is added to the ㄹ irregular verb.
e.g. 놀다(to play) / 놀+까요?→ 놀까요?
어느 곳에서 만날까요? (I) wonder where (I/we) should meet.
It is used to express the probable future.
For a stem that ends in a consonant, use -을 거예요.
e.g.잡다(to catch) / 잡+을거예요→ 잡을거예요.
A stem ends in a vowel, use -ㄹ 거예요.
e.g.타다(to ride) / 타+ㄹ 거예요→ 탈 거예요.
A stem ends in ㄹ irregular, use -거예요.
e.g.밀다(to push) 밀+거예요→ 밀거예요.
듣다 to listen
열다 to open
신다 to wear
보다 to see; to watch
배우다 to learn
달다 to hang
만들다 to make
불다 to blow up
It also indicates the speaker's intention to do something in the future. Especially when the subject is the first person, it shows his/her very strong intention, and it is likely to be true. The verb 'will' in English shares the same meaning with –으ㄹ거예요.
매일 아침 조깅 할 거예요. (I) will jog every morning.
오늘 숙제를 끝낼 거예요. (I) will finish homework today.
장학금을 꼭 받을 거예요. (I) will win a scholarship for sure.
When the subject in the sentence is the third person, the -으ㄹ거예요 represents the speaker's conjecture.
이번 크리스마스는 화이트 크리스마스일 거예요.
제이는 피터의 집에 있을 거예요.
밤에 비가 올 거예요.
시험이 아주 쉬울 거예요.
When -으ㄹ거예요 is used with -이다, the sentence indicates a probable present.
제시는 대학생이에요. Jesse is a college student.
그 모자는 메리 것이에요. The hat is Mary's (thing).