  In this diploma thesis we discuss the deformation theory of Lie algebroids
and Dirac structures. The first chapter gives a short introduction to Dirac
structures on manifolds as introduced by Courant in 1990. We also give some
physical applications of Dirac structures. In the second chapter we present the
deformation theory of Lie algebroids following a recent work of Crainic and
Moerdijk. We discuss the subject from three different points of view and show
the equivalence of these different interpretations. In the third chapter we
give definitions for smooth and formal deformations of Dirac structures on
Courant algebroids. To investigate the formal theory, we write the Courant
bracket with the use of the Rothstein super-Poisson bracket as a derived
bracket. As the main result we show that the obstruction for extending a given
formal deformation of a certain order lies in the third Lie algebroid
cohomology of the Lie algebroid given by the undeformed Dirac structure.
