  Four lectures given at Nankai Institute of Mathematics, Tianjin, China, 5--13
April 1991 present an elementary introduction into the quantum integrable
models aimed for mathematical physicists and mathematicians. The stress is made
on the algebraic aspects of the theory and the problem of determining the
spectrum of quantum integrals of motion. The XXX magnetic chain is used as the
basic example. Two lectures are devoted to a detailed exposition of the
Functional Bethe Ansatz --- a new technique alternative to the Algebraic Bethe
Ansatz --- and its relation to the separation of variable method. A possibility
to extend FBA to the $SL(3)$ is discussed.
