In this chapter, non-dynamical Berry phases are introduced. These are phases due to parameter variations and are related to the geometry of the paths traced out by states in Hilbert space. There are strong analogies between Berry connections and Berry curvatures on one hand and field-related quantities in electromagnetism on the other. So to display these more clearly, an introduction to the gauge theory of electromagnetism is also given, before discussing several examples of Berry phases in optical and quantum systems.