In meta-learning an agent extracts knowledge from observed tasks, aiming to facilitate learning of novel future tasks. Under the assumption that future tasks are `related’ to previous tasks, representations should be learned in such a way that they capture the common structure across learned tasks, while allowing the learner sufficient flexibility to adapt to novel aspects of a new task. We present a framework for meta-learning that is based on generalization error bounds, allowing us to extend various PAC-Bayes bounds to meta-learning. Learning takes place through the construction of a distribution over hypotheses based on the observed tasks, and its utilization for learning a new task. Thus, prior knowledge is incorporated through setting an experience-dependent prior for novel tasks. We develop a gradient-based algorithm, and implement it for deep neural networks, based on minimizing an objective function derived from the bounds, and demonstrate its effectiveness numerically. In addition to establishing the improved performance available through meta-learning, we demonstrate the intuitive way by which prior information is manifested at different levels of the network.