There are nine!
The three major seas are the Mediterranean Sea, the Black Sea (in the upper right), and the Red Sea (in the lower right.)
Four smaller seas are part of the northern Mediterranean: the Tirreno (Tyrrhenian) Sea, the Adriatic Sea, the Ionian Sea, and the Aegean Sea.
The Sea of Marmara links the Black and Aegean Seas.
The tiny, landlocked Dead Sea (bet you forgot about this one!) is visible above the Red Sea in the lower right of the image.