The terms “braid” and “braid groups” were coined by Artin, 1925. In his paper, an n-braid appears as a specific topological object. We consider two parallel planes in euclidean 3-space which we call respectively the upper and the lower frame. We choose n distinct points U v (v = 1, ..., n) in the upper frame and denote their orthogonal projections onto the lower frame by L v . Next, we join each U v with an L μ by a polygon which intersects any plane between (and parallel to) the upper and lower frame exactly once. These polygons are called strings. We assume that they do not intersect anywhere, and that v → μ(v) is a permutation of the symbols 1, ..., n. By removing the strings from the slice of 3-space between upper and lower frame, we obtain an open subset of 3-space the isotopy class of which we call an n-braid. We define a composition between n-braids by hanging on one n braid to the other one. (This can be done by identifying the upper frame of the second braid with the lower frame of the first one, removing these two frames and compressing the slice of 3-space between the first upper and the second lower frame by an affine transformation to the same thickness as before.) Under this composition, the n-braids form a group B n which has n − 1 generators σ v . These are represented respectively by braids which have a projection onto a plane perpendicular to the frames in which the v-th and (v+l)-st string seem to cross once whereas all other strings go straight through as line segments orthogonal to both frames. The braid represented by n strings which go straight through is the representative of the unit element of B n . (Figure 1 shows a representative of the particular 3-braid σ1σ 2 −1 σ1σ 2 −1 .) Of course, this rather vague definition of B n can be made rigorous. See Artin 1947a, Burde 1963.