Good resource for learning braid theory?

Question

I recently heard about braid theory and read the Wikipedia article on it, and it seems really beautiful. What is a good resource for learning more about it?

I have a background in mathematics at the undergraduate level—I took introductory courses on combinatorial topology and abstract algebra (I definitely found the latter quite difficult).

Answer 1

There are a few ways you can approach the subject. I personally went via the algebraic topology route which you may find useful if you know something about the fundamental group/manifolds/higher homotopy groups. I wrote a little about a few resources (definitely not exhaustive) here. The first two references are algebraic topology-based. The third, more accessible and elementary, reference only relies on a background in a small amount of group theory and linear algebra.

For your convenience I'll leave those references below:

J. S. Birman Braids, Links and Mapping Class Groups, Annals of Mathematical Studies 82, Princeton University Press, 1975.

V. L. Hansen, Braids and Coverings, London Mathematical Society Student Texts 18, Cambridge University Press, 1989.

K. Murasugi & B. Kurpita, A Study of Braids, Kluwer Academic Publishers, 1999.

Answer 2

There is this nice playlist by youtuber "Ester Dalvit" on this topic. See here