  The study of the Schr\"{o}dinger equation with the position-dependent
effective mass has attracted a lot of attention, due to its applications in
many fields of physics, including the properties of the semiconductors,
semiconductor heterostructures, graded alloys, quantum liquids, Helium-3
clusters, quantum wells, wires and dots etc. In the present work we obtain
several classes of solutions of the one-dimensional Schr\"{o}dinger equation
with position-dependent particle mass. As a first step the single particle
Schr\"{o}dinger equation with position-dependent mass is transformed into an
equivalent Riccati type equation. By considering some integrability cases of
the Riccati equation, seven classes of exact analytical solutions of the
Schr\"{o}dinger equation are obtained, with the particle mass function and the
external potential satisfying some consistency conditions.
