  The quantum integrable systems associated with the quantum loop algebras
$\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The
factorized form of the transfer operators related to the infinite dimensional
evaluation representations is found and the determinant form of the transfer
operators related to the finite dimensional evaluation representations is
obtained. The master $TQ$- and $TT$-relations are derived. The operatorial $T$-
and $Q$-systems are found. The nested Bethe equations are obtained.
