This will be an introductory talk on the notion of regular rings. Starting from the definition, we will cover various examples and properties of regular rings. We will also see different ways to characterize regular (local) rings including the Auslander-Buchsbaum-Serre criterion, Kunz's Theorem (in positive characteristic), the Cohen-Structure Theorem (in the equal characteristic case) and equivalence with smoothness (for coordinate rings of affine varieties). The talk will only assume familiarity with concepts from Math 614. Speaker(s): Swaraj Pande (UM)