Completely isolated, Pisa's Cathedral stands on a large platform with stairs, like the temples of antiquity. Thus you can walk entirely around it, which I strongly recommend doing, to observe its decorative details and enjoy the fascinating variations of light and shadow on its marble surfaces.
Work on this Romanesque masterpiece dedicated to Santa Maria Assunta began in 1063. On the left side of the church you can see a Latin inscription solemnly recalling the event with the words: "This church was built by the citizens of Pisa: powerful, courageous, and famous".
As often happens in the great medieval cathedrals, its construction began at the back and ended with the façade over a century later. Its architecture will become the model for the entire Campo dei Miracoli, and some of its elements will be recreated in all the other square's monuments: simple volumes, overlapping arches, white and black striped marble, precious geometric inlays with recessed circles and diamonds in the walls.
Walking around the church, you might wonder about the strange dome that dominates it at the intersection between the main body and the transverse one: it has an elliptical shape with a bulbous tip that reminds you of Islamic architecture. And there's another Eastern detail in the sculpture of an imaginary animal: the bronze griffon you can see on the roof.
You could spend hours studying the walls with their bas-reliefs, inlays of multicolored marble, mosaics, and bronze objects: many of these objects come from the spoils of the famous battle against the Turks in Palermo, which is the reason for the square's creation. But keep in mind that many of the external sculptures are only copies: you can admire the originals in the Cathedral Museum.
I suggest carefully looking at the bronze doors at the entrance of the façade: the oldest and most important is at the bottom on the right and is called San Ranieri, after the patron saint of the city. The doors date back to 1180 and depict episodes of the life of Jesus with simplicity and effectiveness, which are commented on with short Latin texts.
FUN FACT: on the Cathedral's exterior opposite the Camposanto there's a marble slab with strange black holes. Legend has it that they are signs left by the devil, who was furious about the Cathedral's construction, and in fact they're called the "devil's scratches".