  We first extend Generalized Differential Calculus (GDC) to higher structures
and create generalized G-invariant bilinear forms. In addition, we also focus
on developing generalized 2- and 3-connection theories in the framework of GDC.
Then, we derive the higher Bianchi-Identities and study the gauge
transformations for those generalized higher connections. Finally, we establish
the generalized 2- and 3-form Yang-Mills theories based on GDC and obtain the
corresponding fields equations.
