Explore the fascinating world of braids and configuration spaces in this 56-minute lecture by Alexander Suciu from Northeastern University. Delve into advanced mathematical concepts as part of the "Advancing Women in Mathematics Across the Americas" series. Learn about topology, homotopy, quotient topology, and unordered configurations. Discover the intricacies of braid groups, fundamental groups, and loop spaces. Examine the relationships between pure braids, color braids, and the swallowtail singularity. Gain insights into the Fox and Fadel theorem and its applications in understanding braid structures.