For a general introduction, I recommend my book with Prof. Barto:

Reinforcement Learning: An Introduction, by Richard S. Sutton and Andrew G. Barto. MIT Press 1998.  Online version. There is also a Japanese translation available.

For a more formal treatment, including rigorous proofs, I recommend the text by Bertsekas and Tsitsiklis:

 Neuro-dynamic Programming, by Dimitri P. Bersekas and John N. Tsitsiklis. Athena Press, 1996.

If you don't have time for a textbook-length treatment, your best bet is one or both of these two papers:

 Reinforcement learning: A survey, by Kaelbling, L.P., Littman, M.L., and Moore, A.W., in the Journal of Artificial Intelligence Research, 4:237--285, 1996.

 Learning and sequential decision making, by Barto, A.G., Sutton, R.S., & Watkins, C.J.C.H., in Learning and Computational Neuroscience, M. Gabriel and J.W. Moore (Eds.), pp. 539--602, 1990, MIT Press.