Florence was the birthplace of the Italian Renaissance. Politically, economically, and culturally it was the most important city in Europe for around 250 years; from some time before 1300 until the early 1500s.
Florentines reinvented money in the form of the gold florin. This currency was the engine that drove Europe out of the "Dark Ages" a term invented by Petrarch, a Florentine whose family had been exiled to Arezzo. They financed the development of industry all over Europe, from Britain to Bruges, to Lyon, to Hungary. They financed the English kings during the Hundred Years War. They financed the papacy, including the construction of the papal palace in Avignon and the reconstruction of St. Peters and the Vatican when the papacy returned to Rome from the "Babylonian captivity".
Dante, Petrarch, and Boccaccio pioneered the use of the vernacular, the use of a language other than Latin. In their case, Tuscan, which, because of them, became Italian. Because Dante, et al., wrote in Tuscan, Geoffrey Chaucer, who spent a lot of time in Northern Italy and who borrowed heavily from Boccaccio's little stories, wrote in English. Others started writing in French and Spanish. This was the beginning of the end of Latin as a common language throughout Europe.
The Florentines, perhaps most notably Filippo Brunelleschi 1377-1466 and Leon Batist'Alberti 1404-1472 invented both Renaissance and neoclassical architecture. These architectural styles revolutionised the way Rome, London, Paris and every other major city in Europe from Barcelona to St. Petersburg were built.
Florentines were the driving force behind the Age of Discovery. Florentine bankers financed Henry the Navigator and the Portuguese explorers who pioneered the route around Africa to India and the Far East. It was a map drawn by the Florentine Paulo del Pozzo Toscanelli, a student of Brunelleschi, that Columbus used to sell his "enterprise" to the Spanish monarchs, and which he then used on his first voyage. Mercator's famous "Projection" is a refined version of Toscanelli's map, taking into account the Americas, of which the Florentine was obviously ignorant. The western hemisphere itself is named after a Florentine writer who claimed to be an explorer and mapmaker, Amerigo Vespucci.
Gallileo and other scientists pioneered the study of optics, ballistics, astronomy, anatomy, and so on. Pico della Mirandola, Leonardo Bruni, Machiavelli, and many others laid the groundwork for our understanding of political science.
Opera was invented in Florence.
And that is just a smidgen of what went on in this city, which never had a population above 60,000 from the first attack of the plague in 1348 until long, long after it became unimportant.
And there were the Medici, perhaps the most important family that ever lived. The Medicis changed the world more than any other family. Forget all the art for which they paid. They taught first the other Italians how to conduct state-craft, and then they taught the rest of the Europeans. Just to cite one example: Catherine de Medici 1519-1589, married Henry II of France reigned 1547-1559. After he died, Catherine ruled France as regent for her young sons and was instrumental in turning France into Europe’s first nation-state. She brought the Renaissance into France, introducing everything from the chateaux of the Loire to the fork. She also was to 16th and 17th century European royalty what Queen Victoria was to the 19th and 20th centuries – everybody’s grandmamma. Her children included three kings of France, Francis II ruled 1559-1560, Charles IX ruled 1560-1574 and Henry III ruled 1574-1589. Her children-in-law included a fourth king of France, Henry IV ruled 1589-1610, plus Elizabeth of Hapsburg, Philip II of Spain of Armada fame, and Mary Queen of Scots.
And that is without mentioning any "artists". From Arnolfo and Cimabue to Giotto, Nanni di Banco, and Uccello; through Lorenzo Ghiberti, and Donatello and Massaccio and the various della Robbias; through Fra Angelico and Botticelli and Piero della Francesca, and on to Michelangelo and Leonardo, the Florentines dominated the visual arts like nobody before or since. And this list does not include many who, in any other place would be considered among the greatest of artists, but in Florence must be considered among the near-great: Benvenuto Cellini, Andrea del Sarto, Benozzo Gozzoli, Domenico Ghirlandaio, Fra Lippo Lippi, Buontalenti, Orcagna, Pollaiuolo, Filippino Lippi, Verrocchio, Bronzino, Desiderio da Settignano, Michelozzo, the Rossellis, the Sangallos, Pontormo, just to name a few. And this list does not include the prolific Ignoto. Nor does it include the near-Florentines, such as Raphael, Andrea Pisano, Giambologna, the wonderfully nicknamed Sodoma and so many more, such as Peter-Paul Rubens, all of whom spent time in Florence and were educated by it.
In 1300, Pope Boniface VIII said that Aristotle was wrong, the universe was made out of five elements, not four: Earth, Air, Fire, Water, and Florentines.
The cathedral topped by Brunelleschi's dome is the third largest Christian church and dominates the skyline. The Florentines decided to start building it in the 1200s. At the outset they were unsure how they were going to do it. It was "technology forcing", not unlike the American Kennedy Administration's decision to put a man on the moon. The dome was the largest ever built at the time, and the first major dome built in Europe since the two great domes of Roman times: the Pantheon in Rome and the Hagia Sophia in Constantinople. In front of it is the medieval Baptistery, where every Florentine was baptized until modern times. The two buildings incorporate the transition from the Middle Ages to the Renaissance in their decoration. In recent years, most of the important works of art from those two buildings and from the wonderful Bell Tower, designed by Giotto, have been removed and replaced by copies. The originals are now housed in the spectacular Museum of the Works of the Duomo, just to the east of the Cathedral.
Florence is filled with many other churches stuffed with some of the finest art in the world: San Miniato al Monte, San Lorenzo, Santa Maria Novella, Santa Trinita, the Brancacci Chapel at Santa Maria della Carmine, Santa Croce, Santo Spirito, SS Annunziata, Ognissanti, and more.
Then there are the art galleries. The Uffizi and the Pitti Palace are two of the most famous picture galleries in the world. But the heart and soul of Florence are in the two superb collections of sculpture, the Bargello and the Museum of the Works of the Duomo. They are filled with the brilliant, revolutionary creations of Donatello, Verrochio, Desiderio da Settignano, Michelangelo, and so many other masterpieces that create a body of work unique in the world. And, of course, there is the Accademia, with Michelangelo's David, perhaps the most well-known work of art anywhere, plus the superb, unfinished prisoners and slaves Michelangelo worked on for the tomb of Pope Julius II.
In all, Florence has something over 80 museums. Among those at the top of most lists are the City hall, the Palazzo della Signoria aka Palazzo Vecchio, a wonderful building with magnificent rooms and some great art; the Archeological Museum, the Museum of the History of Science, the Palazzo Davanzatti, the Stibbert Museum, St. Marks, the Medici Chapels, the Museum of the Works of Santa Croce, the Museum of the Cloister of Santa Maria Novella, the Zoological Museum "La Specola", the Bardini, and the Museo Horne. There is also a wonderful collection of works by the modern sculptor, Marino Marini, in a museum named after him. If you are interested in photography, you should not miss the superb collection of works by the early photographers, the Alinari brothers. The magnificent Strozzi Palace is the site of many special exhibits
To get a great overview of the city, you have plenty of choices: climb the dome of the Cathdral or Giotto's Bell Tower which is much easier or head for Piazzale Michelangelo a large parking lot on the hillside just south of the center of town, or climb a bit further to the church of San Miniato al Monte, a sublime 11th century masterpiece, with superb Renaissance scultpures. At vespers, the monks add to the beauty with chants.
There are also a few places to buy things, from the high-end jewelry stores lining the Ponte Vecchio to some of the most famous shops in the world; Gucci, Pucci, Ferragamo, Valentino, Prada, Armani, Ermenegildo Zegna, Buccellati, Frette, as well as many more wonderful shops that aren't yet world famous. It is increasingly difficult to find bargains, but keen-eyed shoppers can still find good deals on smaller, side streets running off of those above and elsewhere in the center of town. The San Lorenzo market is now largely for tourists. There are also a couple of collections of "outlets" in the suburbs.
Great places to walk include along the Arno and across any of its bridges; through narrow, medieval back streets in the Santa Croce area; and in the Oltr'Arno - on the south side of the river, in many ways like Rome's Trastevere or Paris's Left Bank - but far, far smaller. There are also superb shopping streets, such as the Via Tornabuoni, the Via del Parione, and the Via Maggio.