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.