We introduce a Task-Level Iterative Learning Control method for dynamic manipulation of ropes. We demonstrate this method on a non-planar rope manipulation task called the flying knot. Using a single human demonstration and a simplified rope model, the method learns directly on hardware without reliance on large amounts of demonstration data or massive amounts of simulation. At each iteration, the algorithm inverts a model of the robot and rope by solving a quadratic program to propagate task-space errors into action updates. We evaluate performance across 7 different kinds of ropes, including chain, latex surgical tubing, and braided and twisted ropes, ranging in thicknesses of 7--25\,mm and densities of 0.013--0.5\,kg/m. Learning achieves a 100\% success rate within 10 trials on all ropes. Furthermore, the method can successfully transfer between most rope types in 2--5 trials. https://flying-knots.github.io