The first half of this talk is an introduction to quasi-Frobenius rings and Frobenius rings; it covers the basic properties and some important characterizations of these rings. The second half of the talk deals with finite Frobenius rings. Two characterizations of finite Frobenius rings due to J. Wood state that a finite ring is Frobenius if and only if it has a ``generating character'' or has the ``extension property''. We outline Wood's proofs of these two characterizations. The proof of the second characterization is based on an approach by Dinh and L\'opez-Permouth.

The first half of this talk is an introduction of partial difference sets (PDS), a well studied subject in combinatorics. Roughly speaking, a PDS is a subset of a finite abelian group satisfying certain character equations. Because the generating character of a finite Frobenius ring R relates the characters of (R,+) with the multiplicative structure of R, finite Frobenius rings are particularly suitable for constructions of PDS. For the second half of the talk,
we describe a joint work by the speaker and A. Nechaev on a construction of finite Frobenius local rings. The construction implies that every finite local ring is a homomorphic image of finite Frobenius local ring. This fact enables us to construct Latin square type PDS in an arbitrary finite abelian p-group.