The classical Cauchy integral is a fundamental object of complex analysis whose
analytic properties are intimately related to the geometric properties of its supporting curve.
In this talk I will begin by reviewing the most relevant features of the classical Cauchy integral.
I will then move on to the (surprisingly more involved) construction of the Cauchy integral for
a hypersurface in Euclidean complex space.
I will conclude by presenting new results joint with E. M. Stein