Palazzo Vecchio, the Florence Town Hall, was originally Palazzo della Signoria. The Senoria was the governing body of medieval and Renaissance Florence.
The tower is off-center because it is built on the foundation of a previous tower while the building was placed over land that once housed a family -- the Uberti who were "rebels and Ghibellines (supporters of the Holy Roman Emperor against the Papacy)" -- so that even if they ever were allowed back in Florence, they could never rebuild on their ancestral land.
People were serious about their grudges in Florence.
Fun Fact: On separate occasions, Cosimo de' Medici "Il Vecchio" (1435) and Girolamo Savonarola (1498) spent time in one of the little cells in the tower. Cosimo got to go home and die of old age; Savonarola and two companions were hanged and burned in the Piazza della Signoria.