In this chapter we study integrals of complex-variable functions over paths. Paths are piecewise continuously differentiable maps from closed intervals to the complex plane. An important result proved in this chapter is an analog of the fundamental theorem of calculus for continuous functions with complex antiderivatives. This analog says that the integral of the derivative of an analytic function is equal to the difference of the values of the function at the endpoints. We also investigate an important question concerning the dependence of an integral on the path of integration.