I recently covered the etymology of capital, but capitol deserves its own blog post. Distinguished from the former because it is a building where a legislature meets, rather than a city, the word capitol comes from Capitolium, the Temple of Jupiter in Rome. In 1698, the building for the General Assembly of Virginia was named after the temple because of architectural similarity, and since then use of the word proliferated. The Capitolium was situated on the Capitoline Hill, one of the seven hills of ancient Rome, and that has an officially uncertain etymology. However, it's likely that the name comes from Latin caput, meaning "head", because we know from an army commander's speech that a human skull was found on top of the hill before the Romans built the temple. Caput would be from Proto-Indo-European kaput, also "head".
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.