What is the meaning of 그럼, is it "then" or "of course"

Question

Answer

Both.
그럼 basically means :"then"or "so" and It also can be used as a positive reply,
for example 
-Are you coming?
-Of course!/Definitely!(그럼)
 ,but it can be used as well when somenone's leaving 
"I should get going now.." /"그럼..."

Answer

It could mean both, so if you have a sentence like this:
A: 같이 갈래? would you like to go with me?
B: 그럼? sure/ of course.
other examples:
A: 준비 됐니?
B: 그럼/ 그럼요 yes, of course

However, if you have a sentence like this:
그럼 먼저 가세요
then go first.
그럼 그렇게 할게
well then, I'll do it.

Answer

It can be both.

1)  "그럼" (as "then")  is similar to saying, "그렇다면" (if this is the case, then...)

2) Less formally,  "그럼" can mean, "it is the case" ("그렇다"). It can possibly mean, "of course", but a more precise translation of this would be, "물론"