On the Cauchy Integral and Jump Decomposition

Following “Boundary Value Problems” by Gakhov, we present basic details of the Cauchy Type Integral and its Jump Decomposition. We also contextualize its place and importance in Geometric Function Theory, and efforts to define these integrals over Quasicircles. Finally, we briefly touch on Faber series in relation to the Jump Problem following the work of H. Tietz.