I like how geography -- so baffling when you first arrive in a place as a stranger -- yields up ideas after a few hours of your putting yourself into it.
The old town is criss-crossed by little streets, no more than alleys, tight canyons of masonry faced by unrevealing little windows and well-locked doors. But then you turn a corner and you're in a piazza; space opens up, maybe just a little; and the buildings open up, too.
You realize, walking these old alleys, why piazzas were so important for the Italians. In the streets, you can't really communicate with more than a couple of others; in the piazza you have room for a crowd. You can throw a party.
On the south, the piazza is bordered by an interesting building, the municipal hall, or Palazzo del Ragion. Above, this is essentially one large room, an amazingly wide and high room with complicated medieval trusses, apparently the place for town debates, policy meetings, banquets, etc. Underneath, at piazza level, is an open portico. Thus you can look right through the building to a smaller piazza beyond. The piazza is both enclosed and permeable at the same time.
What you reach by going through the portico is the religious center of town -- the Piazza del Duomo, with its cathedral as well as a very large Romanesque church of Sta. Maria Maggiore, baroque-ified inside to beat the band. Literally next to this is a third church, a chapel that holds the tomb of Bartolomeo Colleoni, a Bergamasque mercenary mostly working in the pay of Venice. ("Bergamasque" is the adjective form of Bergamo, and became used for a famous Renaissance dance.)
So beyond the portico lie two big forms of organized power - church and army. But back in the big piazza, power seems much more diffused: library, university, commerce, city government with its traditional neighborly squabbles.
History layers itself: Medieval (a town walling itself in for its own life in a fierce environment of marauders); Renaissance (Colleoni putting his energy and guts -- sprezzatura, he'd have said -- up for sale to the Venetian Republic); Enlightenment: a rationalist creates a visual emblem of the predictability of Galilean planetary motion.