The capital of the Slovak Republic is Bratislava.

An excerpt from the article 37 facts about Slovakia

It is also the largest city in Slovakia in terms of population (437.726 people). Bratislava is located on the Danube (it stretches on both banks) near the border with Austria and Hungary. Due to this location, it is the only capital in the world that borders two countries. The city is the seat of the highest state authorities. It is also the center of cultural, social, economic, and political life. Bratislava has many valuable monuments. It houses, among others, the Gothic cathedral of St. Martin, which was the coronation place of Hungarian kings for 300 years.