via this
and this

Here is a very biased list of books and links that I found useful for students entering our lab (other labs may emphasize different aspects though):

Theoretically optimal universal stuff:

  • M. Hutter (ex-IDSIA): Universal Artificial Intelligence. THE book on mathematically optimal universal AI / general problem solvers / universal reinforcement learners (goes far beyond traditional RL and previous AI methods)

  • Overview sites on universal RL/AI and Goedel machine and optimal program search and incremental search in program space

  • M. Li and P. M. B. Vitanyi. An Introduction to Kolmogorov Complexity and its Applications (2nd edition). Springer, 1997. THE survey of algorithmic information theory, based on the original work by Kolmogorov and Solomonoff. Foundation of universal optimal predictors and compressors and general inductive inference machines.