This course will provide an introduction to dynamics of rational functions over number fields, focusing on questions about heights and preperiodic points. Topics will include an introduction to complex dynamics, dynamics over local fields, the basics of heights on varieties, canonical height functions, bounds on the number of rational preperiodic points, and the action of Galois on preperiodic points. If time permits, we will also discuss dynamics on higher-dimensional varieties (e.g., Henon maps) and connections to "unlikely intersections." The course will be as self-contained as possible, but familiarity with algebraic number theory, elliptic curves, complex analysis, local fields, and basic algebraic geometry will all be useful.