The book "Properties of Closed 3-Braids and Braid Representations of Links" offers a comprehensive examination of various aspects of braid representations in relation to knots and links. It presents complete classification results for several properties illustrated by Xu's normal 3-braid form and the Hecke algebra representation theory of link polynomials developed by Jones. The work identifies topological link types within the closures of 3-braids that exhibit a specific Alexander or Jones polynomial. Furthermore, additional classifications of knots and links arising from the closure of 3-braids are addressed, and new results concerning 4-braids are also part of the investigation. The book is aimed at knot theorists, topologists, and graduate students, providing effective techniques for analyzing diagrammatic examples with unexpected properties.