A topic within Topology, itself one of 11 topics in that field and part of Mathematics.
No prior grounding assumed.
The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
Colin C. Adams · 1994
Introduces knot theory through diagrams and hands-on invariants rather than algebraic machinery, arguing the subject is learnable, and full of open…
Primary sources and full treatments.
Topological Invariants of Knots and Links
James W. Alexander · 1928
Constructs a polynomial invariant from a knot's diagram that is provably unchanged by Reidemeister moves, giving the first computable tool for…
+1 more at this level
3 works
Colin C. Adams
Introduces knot theory through diagrams and hands-on invariants rather than algebraic machinery, arguing the subject is learnable, and full of open problems, without a graduate topology course first.
James W. Alexander
Constructs a polynomial invariant from a knot's diagram that is provably unchanged by Reidemeister moves, giving the first computable tool for telling two knots apart.
link checked 17 Sept 2026Vaughan F. R. Jones
Discovers a new knot polynomial by an unexpected route through operator algebras, arguing that representations of the braid group inside a von Neumann algebra carry more information about a link's isotopy type than any diagram-based invariant then known.
link checked 17 Sept 2026