Perhaps surprisingly given the small size of their brains, spiders are reasonably adept at learning. We have published a number of papers on spider learning. For example, Chad Hoefler (now at Arcadia University) published on the ability of jumping spiders to associate their nest locations with their retreat sites; Christa Skow's dissertation focused on their ability to attend to contextual (background) cues when learning tasks; and we've used aversive conditioning (e.g., Julie Bednarski's work) to steer spiders away from particular types of video stimuli. Here are some papers that focus on or include some elements of learning. Undergraduate co-authors are underlined.
Jakob, E.M. and S. Long. In press. How (not) to train your spider. Invited paper for Festschrift issue of New Zealand Journal of Zoology.
Long, S.M., A. Leonard, A. Carey, and E. M. Jakob. 2015. Vibration as an effective stimulus for aversive conditioning in jumping spiders. Journal of Arachnology 43:111-114.
Long, S. M., S. Lewis, L. Jean-Louis, G. Ramos, J. Richmond, and E. M. Jakob. 2011. Firefly flashing and jumping spider predation. Animal Behaviour 83:81-86.
Jakob, E. M., C. Skow and S. Long. 2011. Plasticity, learning and cognition. In M. E. Herberstein (ed.), Spider Behaviour: Flexibility and Versatility. Cambridge University Press. Pp. 307-347.
Jakob, E., C. Skow, M. Haberman, and A. Plourde. 2007. Jumping spiders associate food with color cues in a t-maze. Journal of Arachnology 35:487-492.
Hoefler, C. and E. Jakob. 2006. Jumping spiders in space: movement patterns, nest site fidelity and the use of beacons. Animal Behaviour 71:109-116.
Skow, C. and E. Jakob. 2006. Jumping spiders attend to context during learned avoidance of aposematic prey. Behavioral Ecology 17:34-40.