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Knots are just simple closed curves in space, say R^3. This is an old topic, but lots of mathematics originated from knot theory, particularly since the middle of 20-th century. Here I would like to give a brief introduction, taking a viewpoint from an arithmetic geometer. 60 years ago, Barry Mazur wrote a note comparing knots with primes, and compact oriented 3-manifolds play roles analogous to number fields. Development of knot theory is closely related to the history of topology, and core mathematics. Gauss and his students started the very topic, and the knot invariants, particularly polynomial invariants, can be now computed from Sage package.