  The intended purpose of this work is to provide the reader with a
comprehensive, state-of-the art presentation of the theory of complex Hadamard
matrices, or at least report on the very recent advances. This manuscript
consists of three chapters, each describing one of three distinct faces of this
field whose treatment require various mathematical tools ranging from
combinatorics, functional analysis to symbolic computation. Although we firmly
believe that these beautiful objects are interesting on their own and worth
investigating from a purely mathematical perspective we make considerable
efforts to highlight some of their applications we aware of.
