  Braid groups are an important and flexible tool used in several areas of
science, such as Knot Theory (Alexander's theorem), Mathematical Physics
(Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this
note we will focus on their algebraic-geometric aspects, explaining how the
representation theory of higher genus braid groups can be used to produce
interesting examples of projective surfaces defined over the field of complex
numbers.
