  This paper is expository and is accessible to students. We define simple
invariants of knots or links (linking number, Arf-Casson invariants and
Alexander-Conway polynomials) motivated by interesting results whose statements
are accessible to a non-specialist or a student. The simplest invariants
naturally appear in an attempt to unknot a knot or unlink a link. Then we
present certain `skein' recursive relations for the simplest invariants, which
allow to introduce stronger invariants. We state the Vassiliev-Kontsevich
theorem in a way convenient for calculating the invariants themselves, not only
the dimension of the space of the invariants. No prerequisites are required; we
give rigorous definitions of the main notions in a way not obstructing
intuitive understanding.
