Universal integrability objects

We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group $U_q(\mathcal{L}({\mathfrak{s}\mathfrak{l}}_2))$. We give a complete set of the functional relations correcting inexactitudes of the previous considerations. A special attention is given to the connection of the representations used to construct the universal transfer operators and $Q$-operators.