This is a tutorial article concerned with problems related to dates and, geometrical alignments determined from astronomical considerations. The mathematical problems often arise in connection with attempts to specifiy days of the year in the past or in connection with ancient edifices. In this way the solutions are of interest to anthropologists, archeologists, art historians, folklorists, historians, and astronomy enthusiasts. While the methods of solution presented are general, specific problems are also employed for illustrative purposes. Some problems involve the famous ancient edifices of Abu Simbel, Cheops' Pyramid, and Stonehenge, and bright celestial objects such as the Sun, Sirius, and the Pleiades. Solutions depend on a knowledge of spherical trigonometry and basic astronomy, and often involve the phenomenon of the precession of the Earth's spin axis. Effects of precession are described geometrically and algebraically.