The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained importance and popularity during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse fields of science and engineering. Indeed it provides several potentially useful tools for solving differential, integral, and integro-differential equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main purpose of this expository article is to provide a rather brief introduction to the theory and applications of fractional calculus.