Is there a term for the 'study of love'?

There is a word 'erotology' which is defined as "the 'science' of love". This is a rarely used word, except in anthropology, where it is found slightly more often. This term really relates to the study of sexual activity and techniques rather than to the study of love itself. The only word this editor can think of for that is 'marriage'!

From: www.askoxford.com