One in a quartet of forts defending Havana harbor, La Punta was designed by Italian military engineer Bautista Antonelli and built between 1589 and 1600. It underwent comprehensive repairs after the British shelled it during their successful 1762 Havana raid. During the colonial era a chain was stretched 250m to the castle of El Morro every night to close the harbor mouth to shipping.
The castle's museum is really just a few information boards chronicling its history (in Spanish), but there are good views from the battlements, where you can also admire the huge Parrott cannons dating from the mid-19th century.