In M.A. Armstrongs book "Groups and Symmetry" in Chapter 12 he introduces the reader to the fascinating topic of Braid Groups.

Does anyone know of a book at undergraduate level (or even a popular book) that deals with Braid Groups.

Can you progress with Braid Groups if you lack a sophisticated knowledge of topology? That is, how far can you progress with a study of Braid Groups if you only have a good knowledge of abstract algebra?