This work introduces a novel set-to-set (STS) iterative learning control (ILC) framework which generalizes the ideas of point-to-point ILC (PTP ILC) and region-to-region (RTR ILC) techniques. The existing ILC frameworks are extended by tracking both sets and points at desired times within an iteration. The objective of the new framework is to optimize control allocation and PTP tracking performance while tracking goal sets at all desired times. Within these goal sets, the tracking is performed without constructing a reference trajectory. Theoretical proof is presented on the improved performance of STS ILC over PTP ILC and RTR ILC, in addition to iterative convergence of the STS ILC input sequence and tracking error. Analysis of the STS ILC demonstrates that by tracking the sets in a reference-free manner, the STS ILC will produce a lower bound on the optimization cost in comparison with the alternative ILC methods. Two multi-input multi-output case studies are used to demonstrate the effectiveness of the STS ILC in allowing a linear system agent to visit polytopic set regions by learning the correct paths from one iteration to the next. Future work envisages developing a theory for the STS ILC for robustness to uncertain and nonlinear plants, considering input constraints, and adopting data-driven methods for modeling the plant.