A torus knot T(p,q) winds p times around the torus meridian and q times along the longitude, parameterized as x=(R+r·cos(qφ))cos(pφ), y=(R+r·cos(qφ))sin(pφ), z=r·sin(qφ). It is the unknot only when gcd(p,q)=1 — otherwise it decomposes into gcd(p,q) separate components forming a torus link. The knot group (fundamental group of the complement) is the braid group B₂ = ⟨a,b | aᵖ=bᵍ⟩. The Alexander polynomial of T(p,q) encodes deep information about the knot's topology and connects to the Jones polynomial via quantum groups.