Short answers, pulled from the story.
The Republic of Florence originated in 1115, when the Florentine people rebelled against the Margraviate of Tuscany following the death of Matilda of Tuscany. Rather than submit to her successor Rabodo, the Florentines formed their own commune.
The florin was a gold coin introduced by Florence in 1252. It became the dominant trade coin of Western Europe for large-scale transactions because of its fixed, reliable gold content, replacing silver bars and being widely imitated across the continent. It was the first European gold coin struck in sufficient quantities to play a significant commercial role since the seventh century.
Cosimo de' Medici gained effective control of Florence in 1434 after the people voted to overturn his exile and banish the Albizzi family who had expelled him. He ruled without holding formal office, controlling elections through influence, patronizing key figures, and using private armies and Milanese troops to suppress opposition, as during the political crisis of 1458.
The Pazzi conspiracy of 1478 was a plot organized by the Pazzi family that resulted in the murder of Lorenzo de' Medici's brother Giuliano. The coup failed, and the conspirators were executed. Pope Sixtus IV, who had supported the plot, excommunicated all of Florence and sent a delegation to arrest Lorenzo, triggering a two-year war that Lorenzo ended through diplomacy.
The Bonfire of the Vanities was an act ordered by Girolamo Savonarola, the priest who governed Florence after the Medici's first expulsion. He commanded that objects he deemed sinful, including wigs, perfume, paintings, and ancient pagan manuscripts, be gathered and burned. Savonarola was himself executed by burning in the Piazza della Signoria in May 1498.
The Republic of Florence effectively ended in 1530, when Emperor Charles V declared himself sole arbiter of Florence's government after an 11-month siege and made the Medici hereditary rulers. A new constitution ratified in 1532 abolished the signoria and gonfaloniere. In 1569, Pope Pius V formally elevated Cosimo I de' Medici to the rank of Grand Duke of Tuscany, marking the republic's official end.