Like many Cathedrals that have a long construction time, 1296-1436 for this one, it had many master builders and artisans. Starting in the Gothic Style by the Arnolfo di Cambio it had progressed through the Romanesque, the Renaissance into the Gothic REVIVAL for its facade. This cathedral was built around a previous cathedral dedicated to Saint Reparata from 393. It was demolished midway through the construction. The beauty of this cathedral is in it's raw presentation of the construction especially after it's exterior embellishment, leaving the interior very simple yet elegant. Having been an early go at this, it has groin vaults and a simple plastered finish. So it's austerity allows you to feel the space without all of the soon to be fashionable Romanesque, And Renaissance complications of Baroque and Rococo. Each of these movements/styles became an exercise in the expansion of the disciplined orders into fashionable visions made possible by the technological enhancements of craftsmanship and skill. Depictions of this cathedral early on would show the raw force of the austere forms. In contrast to later churches, a lot of the field finishes in each quadrant of the vaults and the walls would became much busier. It wasn't until the mid 19th century that the polychromatic facades were added. Noting that this was long afterwards in the Gothic REVIVAL period by Emilio De Fabris. As I mentioned in my review of the Milano Duomo, the power and control over the tendering of these designs to architects led to long periods of delay while the apprentices or transitional master builders could replace the previous one. A few times as architects died and for the black death construction was paused. It's a fascinating story to investigate. Wikipedia has a great summary for your review.

The nave and the apse, the two crossing aisles that intersect at the transcept, were finished first. But the dome above the transcept stood without a cover for a time. In fact the actual engineering for the dome was not even thought of prior to Brunilescci winning the competition. Of course he was backed by the Medicis so, well you know, money, money, money. The intriguing point about Brunalleschi's solution was complex. Using an inner and outer dome, the progress was done without inner supports underneath. The principle is not just stepping masonry inward with each rise across a decreasing slope as it rises, (like at the Pantheon but elliptical), but it involves a connection between the inner and outer dome.

This connection helps the outward forces by acting like a truss. Because only at these connecting points you have reactions to the gravity from the weight of the masonry, you do not have that mass of those connection components. This is the basic principle of trusses. With a beam the longer the span the deeper the beam. With a trust, you can eliminate material & cost as well. For this application the elimination of the mass allows for the masonry to do its job without having to be overly thick in dimension. I believe to this day it's the largest masonry done so he did something correct.

You can see the Nave and side aisles for free, but still usually a line. For the Coupola you will need tickets in advance as well for the Campanile Tower, each will have their own lines just as long. Note that on your trip up, you will go between the inner and outer dome and move inward as you work your way around the connection points between each dome structure.

Recommend getting there BEFORE your time. Also if you're looking for the shot to take home, arrive before 7am~ish to have an unobstructed picture. Puddles on the stone make a good mirror effect for a "from the ground" shot too. This is a can't miss site to see.