Metamaterials are basically periodic structures. As such they can be analyzed by means of Bloch waves. This approach has limitations due to the existence of losses but provides very interesting insights into the properties of metamaterials. Moreover, a very good understanding of Bloch theory is fundamental for such advanced topics as photonic topological insulators. In view of this, an elementary introduction to the theory of fiber bundles is provided, so as to be able to define what a Chern number is. The chapter also covers the notion of geometric phase, associated with the names of Pancharatnam, Rytov, and Berry.