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An exterior differential calculus in the general framework of generalized Liealgebroids is presented. A theorem of Maurer-Cartan type is obtained. Allresults with details proofs are presented and a new point of view over exteriordifferential calculus for Lie algebroids is obtained. Using the theory oflinear connections of Ehresmann type presented in the firstt reference, theidentities of Cartan and Bianchi type are presented. Supposing that any vectorsubbundle of the pull-back Lie algebroid of a generalized Lie algebroid isinterior differential system (IDS) for that generalized Lie algebroid, then theinvolutivity of the IDS in a theorem of Frobenius type is characterized.Extending the classical notion of exterior differential system (EDS) togeneralized Lie algebroids, then the involutivity of an IDS in a theorem ofCartan type is characterized.

Intersection between the geometry of generalized Lie algebroids and some aspects of interior and exterior differential systems