From the Piazza del Campo or the main square of Siena, you can walk to the Siena Cathedral or the Duomo (Santa Maria Assunta or Most Holy Mary of Assumption), although it might be quite uphill in some parts (one, in particular, is a bit scary to climb if you are not wearing comfortable shoes).
The cathedral is a wonderful example of Italian Romanesque-Gothic architecture. The façade is just gorgeous, and the interior is decorated in fascinating black and white stripes and floor mosaics. The ceiling is decorated with stars.
Don't forget to take a look inside the Piccolomini Library with its magnificent ceiling and walls, and to take note of one of the steps to the Baptistery where a small cross marking where St. Catherine was tempted by the devil can be found.
The cathedral opens at 1030, so do not go there too early. The ticket to see only the cathedral costs about EUR3. In front of the cathedral is the Hospital of Santa Maria della Scala, which used to be the oldest functioning hospital in Europe.
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