The aim of this book is to present recently discovered connections between Artin's braid groups En and left self-distributive systems (also called LD- systems), which are sets equipped with a binary operation satisfying the left self-distributivity identity x(yz) = (xy)(xz). (LD) Such connections appeared in set theory in the 1980s and led to the discovery in 1991 of a left invariant linear order on the braid groups. Braids and self-distributivity...