The Mediterranean Sea is sub-divided into a number of smaller seas, each with their own designation (from west to east). The ferries are - as far as possible - ordered by sea which they traverse.
Please add website links, sailing frequencies, sailing durations, discounts. As the purpose of this page is to provide travellers who want to cross the Med with info, while adding, focus on international lines, instead of meticulously adding small ferries connecting island to the mainland.
Navibulgar (Navigation Maritime Bulgare) German-Bulgarian owned company has two vessels and according to their website they provide passenger transportation between Varna - Odessa Ilichevsk - Poti/Batumi - Ilichevsk - Varna .
From Russian port of Sochi ferries go to Trabzon (Turkey) and Batumi (but you have to be a citizen of Georgia, Russia or CIS to board this one). Website of the port in Sochi 
This is a usable article. It touches on all the major areas of the topic. An adventurous person could use this article, but please plunge forward and help it grow!