1. The pattern '-(으)ㄹ까요?'
2. The Propositive '-(으)ㅂ시다'
3. The Connective '-(으)러'
4. The pattern '-(으)ㄹ게요'
1. The pattern' -(으)ㄹ까요?' Shall we(I) ~ ?/Will it be ~ ?
   
  The pattern '-(으)ㄹ까요?' is used to express inquiring about someone's opinion, view or appraisal on a certain matter or fact with the action verb.
In this case, the subject of the sentence is always the first person, singular or plural.
   
 
  우리 거기에서 만날까요? Shall we meet there?
  무엇을 할까요? What shall I do?
  늦었으니까 비행기로 갈까요? Because we are late, shall we go by airplane?
   
  When used with the adjectives, or with '있다(to exist)' or '이다(to be)', the subject of the sentence is the third person, and it express doubt or polite denial.
   
 
  한국어가 가 재미있을까요? Will Korean be interesting?
(or You say Korean is interesting ?)
  이게 더 나을까요? Will this one be better?
  도서관이 저기에 있을까요? Will the library be over there?
(Do you think the library is over there?)
   
 

   
2. The Propositive '-(으)ㅂ시다' : let's --(propositive)
   
  This form is used to expressing the subject's suggestion with the action verbs and the verb of existence '있다'. It cannot be used with '이다' nor with adjectives.
   
 
  빨리 갑시다. Let's go quickly.
  한국어를 공부합시다. Let's study Korean.
  여기에 있읍시다. Let's stay here.
  기차로 갑시다. Let's go by train.
  이번 주말에 만납시다. Let's meet this weekend.
   
  '- 읍시다.' is used after verb stems ending in a consonant.
   
 
먹(다) + -읍시다 ; 먹읍시다.
   
  '- ㅂ시다.' is used after verb stems ending in a vowel.
   
 
가(다) + ㅂ 시다 ; 갑시다.
   
  In plain speech style(반말), with children and sometimes with close friends you can use the form '-자' instead of '-아/어/여'.
Drop the '-요' of the informal polite speech style ending '-아/어/여요'. Here are some examples;
   
 
  빨리 가자. Let's go quickly.
  한국어를 공부하자. Let's study Korean.
  여기에 있자. Let's stay here.
  기차로 가자. Let's go by train.
  이번 주말에 만나자. Let's meet this weekend.
   
 

   
3. The Connective '-(으)러' : in order to
   
 

The connective '-(으)러' is used to express the purpose of the subject's action and is followed by either '가다'(to go), '오다'(to come) or their compounds, or any verb which indicates movement, such as '다니다'(to go and come regularly).
   
 
  저는 어제 책을 사러 서점에 갔어요. I went to a bookstore (in order) to buy a book yesterday.
  (저는) 공원에 운동하러 왔어요. I came to the park (in order) to exercise.
 
수영하러 갈까요?
Shall we go for a swim?
 
탐이 놀러 올 거예요.
 Tom will come (in order) to play.
   
  As you see the above examples, '-러' is used after verb stems ending in a vowel or the consonant 'ㄹ'. On the other hand, '-으러' is used after verb stems ending in all consonants except 'ㄹ'.
Tense and negation are expressed with the verbs 가다 or 오다, but not in the verb connected to '-(으)러'.
   
 
  안나씨는 책을 사러 갔어요 Anna went to buy a book.
  안나씨는 밥을 먹으러 가지 않았어요. Anna didn't go to eat.
   
 

   
4. The pattern '-(으)ㄹ게요' : I will do --
   
  This form is used for expressing the speaker's intention or plan or promise. It is used with action verbs as well as with the verb 있다, but not with adjectives.
   
 
  제가 할게요. I will do it.
  거기에서 기다릴게요. I will wait (for you) over there.
 
내일 갈게요.
I will go tomorrow.
 
제가 도와 드릴게요.
 I will help you.