Partial actions of groups on algebras have been studied and applied first in C*-algebras and then in several other areas of mathematics. In a pure algebraic context they were recently introduced and studied by M. Dokuchaev and R. Exel in Trans. Amer. Math. Soc. 357 (2005). In this lecture(s) we will present an introduction to the subject and will consider related questions like partial skew group rings, partial skew polynomial rings, etc.