This book is based on a graduate course taught by the author at the University of Maryland. The work falls into two strands: first the elementary theory of Artin Braid groups is developed and the link between knot theory and the combinatorics of braid groups is discussed through Markov's theorem; this is followed by an investigation of polynomial maps.

This book is based on a graduate course taught by the author at the University of Maryland, USA. The lecture notes have been revised and augmented by examples. The work falls into two strands. The first two chapters develop the elementary theory of Artin Braid groups both geometrically and via homotopy theory, and discuss the link between knot theory and the combinatorics of braid groups through Markov's Theorem. The final two chapters give a detailed investigation of polynomial covering maps, which may be viewed as a homomorphism of the fundamental group of the base space into the Artin braid group on n strings. This book will be of interest to both topologists and algebraists working in braid theory.