Hypergeometric systems are systems of linear partial differential equations in several variables that generalize confluent and non confluent classical hypergeometric equations in one variable. They are associated with a full rank matrix A with integer components and a vector of complex parameters. These systems play the same role in Theory of D-modules as toric varieties in Algebraic Geometry and they are both related. The study of this systems involves different areas such as analysis, algebra and combinatorics. We study the irregularity of this systems via Gevrey solutions and cohomology of the irregularity complex.