  We explore the set of unitary matrices characterized by a given structure in
the context of their applications in the field of Quantum Information. In the
first part of the Thesis we focus on classification of special classes of
unitary matrices and possibility of introducing certain internal
parameterizations. Several new results and conjectures are discussed. Second
part of the Thesis is devoted to the concept of multipartite quantum
entanglement. We present a solution to the problem of absolutely maximally
entangled states of four subsystems with six levels each. Finally, we analyze
the excess of a matrix and the corresponding Bell inequalities. This
combination allows us to draw new conclusions related to quantum nonlocality.
