The Baptistery of San Giovanni in Fonte is considered the oldest in the Western hemisphere, even older than that of San Giovanni in Laterano in Rome. It was founded by Bishop Severus at the end of the fourth century, and its architecture has a vaguely oriental flavor with a square layout that turns into an octagon closed by a dome at the top. Make sure you don't miss the fragments of the mosaics with scenes of Jesus's life in a classical style, which reveal their Byzantine art inspiration.
