Learner's definition of CORRESPONDENCE
1 : the activity of writing letters or e-mails to someone
2 [noncount] : the letters or e-mails that people write to each other
A book of the author's personal correspondence was published early last year.
A formal tone is always used in business correspondence.
I have a pile of correspondence [=letters from people] on my desk.
3 : a direct relationship to or with something or between two things
4 : the fact of being similar or equal to something