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After a short introduction to Lie algebroids, the work introduces Courant algebroids as well a the Superlanguage to describe their Q-structure. We continue with computation of the Courant cohomology for certain regular Courant algebroids. The thesis closes with the definition and numerous examples of matched pairs of Courant algebroids. Examples arise from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids.