Hello. How are you? I hope you're having a great time. I'm finishing my college exams these days and then, classes will start again. How is Greek learning going? I hope you will come to us next summer. See you again. Many kisses!
See you again does imply to either talk or see (meet). As this obviously is a letter/e-mail, communication is done by writing. See you again as in "meet you again" is more appropriate. Also, the author is referring to his/her wish for a visit of the reciever of the letter/e-mail next summer.