Gromov introduced the notion of hyperbolic groups in 1987, and the study of hyperbolic groups has been thriving since then. Roughly speaking, a hyperbolic group is a finitely generated group of which the Cayley graph has certain hyperbolic feature on a large scale. In this talk, I will introduce the large scale versions of some geometric notions, such as isometry, convexity, and hyperbolicity, and give examples, non-examples, and properties of hyperbolic groups. If time allows, I will talk about some applications of hyperbolic groups to low-dimensional topology.