  Basic concepts of quantum integrable systems (QIS) are presented stressing on
the unifying structures underlying such diverse models. Variety of ultralocal
and nonultralocal models is shown to be described by a few basic relations
defining novel algebraic entries. Such properties can generate and classify
integrable models systematically and also help to solve exactly their
eigenvalue problem in an almost model-independent way. The unifying thread
stretches also beyond the QIS to establish its deep connections with
statistical models, conformal field theory etc. as well as with abstract
mathematical objects like quantum group, braided or quadratic algebra
