This chapter is devoted to rings. After some basic definitions, attention is moved to examples of rings, including group rings, polynomial rings, Laurent series and power series. Then ideals and quotient rings are discussed, with the interplay between maximal ideals and simple rings. Rings given by generators and relations are studied, as well as twisted rings. The final part of the chapter concerns unique factorization in principal ideal domains. Close relatives of such rings, like Euclidean domains and unique factorizations domains, are also