  This doctoral thesis studies the overlap between two well-known collections
of results in number theory: the theory of periods and period polynomials of
modular forms as developed by Eichler, Shimura and Manin and its extensions by
K\"ohnen and Zagier, and the theory of 'multiple zeta values' (MZV's) as
initied by Euler and studied by many authors in the last two decades. These two
theories had been linked by Manin, who introduced 'multiple L-values' (MLV's).
We propose to study those families of number and especially the relations among
them, generalizing the Eichler-Shimura-Manin relations, and also linked some of
those MLV's to MZV's.

Number Theory