When Florence decided to build a cathedral dome in 1296, nobody knew how. The octagonal hole was 42m wide — wider than the Pantheon's. No buttresses. No centering (wooden support). Impossible. In 1418, Filippo Brunelleschi won the competition with a design he refused to fully explain (afraid of theft). He built 2 nested shells of self-supporting herringbone brick that lock together without centering. Engineers didn't fully understand HOW until the 20th century. You can climb 463 steps between the two shells, see Vasari's Last Judgment frescoes from 3 meters away, and emerge at the lantern with Florence below you.
The Dome climb (€30 Brunelleschi Pass, book on duomo.firenze.it): 463 steps, no elevator. Between the two shells you walk on narrow stairs with the frescoed interior dome curving above your head — Vasari and Zuccari's Last Judgment (1572-79, 3,600m²) fills the entire surface. At eye level you see individual demons and damned souls from 3 meters. At the top: the lantern terrace — 360° view. Book 1-2 weeks ahead. Giotto's Campanile (€20 or included in pass): 414 steps, wider staircase, the BEST dome photo (you see the dome from the side, Florence below). The Baptistery (included): Ghiberti's Gates of Paradise (copies — originals in the Museo dell'Opera). Golden mosaic ceiling inside (Byzantine, 13th century).
Practical: Piazza del Duomo. Brunelleschi Pass €30 (dome + campanile + baptistery + museum + crypt). Book on duomo.firenze.it. Best slot: Dome at 8:30am (first, fewest people). Cathedral entry: free (no booking).