It was written by Joan Birman, based on lecture notes by James W. Cannon,[1] and published in 1974 by the Princeton University Press and University of Tokyo Press, as volume 82 of the book series Annals of Mathematics Studies.

Although braid groups had been introduced in 1891 by Adolf Hurwitz and formalized in 1925 by Emil Artin,[1] this was the first book devoted to them.

[2] This is a book for advanced mathematics students and professionals, who are expected to already be familiar with algebraic topology and presentations of groups by generators and relators.

[1] Reviewer Lee Neuwirth calls the book "most readable", "a nice mix of known results on the subject and new material".

[2] Wilhelm Magnus finds it "remarkable" that while covering the subject with full mathematical rigor, Birman has preserved the intuitive appeal of some of its earliest works.