Publisher This chapter discusses partially resolvable t-partitions. The chapter discusses primarily with the case |P|= 1, |S| = 1. The corresponding partially resolvable t-partitions are denoted by PRP t-(p, s, υ ; m) provided P = {p}, S = {s}. These designs are interesting on their own and they also arise naturally in many instances, for example, when considering embeddings of Steiner triple systems, Doyen and Wilson, recursive constructions for Steiner quadruple systems, Lindner and Rosa, and other occasions. Necessary conditions for the existence of PRP t-(p, s, υ; m) are discussed and some general results and constructions are presented. The chapter also discusses the existence of PRP t-(p, s, υ; m) in the two smallest non-trivial cases, that is, when t = 2, p = 2, s = 3, and t = 2, p = 3, s = 2, respectively. The case of PRP 2-(2, 4, υ; m) is discussed. Two examples of partially resolvable 3-partitions are given in the chapter.