The braid group Bₙ has generators σ₁,…,σₙ₋₁ where σᵢ crosses strand i over strand i+1. Relations: σᵢσⱼ = σⱼσᵢ (|i−j|≥2) and σᵢσᵢ₊₁σᵢ = σᵢ₊₁σᵢσᵢ₊₁ (braid relation). The closure of a braid gives a knot or link. Garside's solution to the word problem: every braid has a unique "left canonical form".
Type a braid word using σᵢ → "si" and σᵢ⁻¹ → "si i" (inverse). Click generators to build the word. The closure connects strand ends back to tops, yielding a knot/link.