  We present an analysis of the structure of Bell inequalities, mainly for the
case of N qubits with two observables each. We show that these inequalities are
related to Hadamard matrices and define Bell polynomials (in one variable) as
an additional tool. With these aids we raise several conditions the
coefficients of Bell inequalities must satisfy, and recursively generate the
whole set of inequalities starting from N=1. Moreover, we prove some
characteristic features of this set, such as that most of the inequalities
contain all expectation values under consideration. Finally, we show how the
presented results can be used to construct Bell inequalities with certain
properties. An outlook on further research topics concludes the paper.
