함께/같이
what is the difference between 함께 and 같이? and how do we use them? Which one is more formal?

Question

Answer

They are same.

친구와 함께 영화관에 갔다. 
친구와 같이 영화관에 갔다. 
I went to the movie theater with my friend.

As for 'formal', it doesn't matter which one you use it.

Answer

함께 and 같이 are almost same in the meaning of "together(with)" 
Both are formal.
But 같이 has another meaning 'like'

Refer to http://www.italki.com/question/92819