Upvote:2
Actually, it began tilting immediately after they started building it. Some years after, construction stopped for about a century because the Republic of Pisa was busy fighting a bunch of wars with its neighbors. When construction resumed, the new architect took the tilt into account and compensated for it by making the walls on each new floor taller on one side. Here's what Wikipedia has to say about it:
In 1272, construction resumed under Giovanni di Simone, architect of the Camposanto. In an effort to compensate for the tilt, the engineers built upper floors with one side taller than the other. Because of this, the tower is actually curved. Construction was halted again in 1284 when the Pisans were defeated by the Genoans in the Battle of Meloria.
Another interesting thing about the tower is that it combines to architectural periods: Romanesque and Gothic.