There are six public and one private university in Estonia. Five of those are in Tallinn and two in Tartu. The oldest and biggest university in Estonia is the University of Tartu with circa 18 100 students followed by Tallinn University of Technology with circa 13 900 students. Both of those universities have colleges also in other cities of Estonia.
Universities and higher education institutions: http://www.investinestonia.com/en/Web-links/Universities-and-HEIs/