Probabilistic Graphical Models: Principles and Techniques by Daphne Koller, Nir Friedman (2009) [book] — The comprehensive reference on graphical models, inference, and learning. (copyrighted)
Causality: Models, Reasoning, and Inference by Judea Pearl (2009) [book] — The mathematical framework for causal reasoning. do-calculus and interventions. (copyrighted)
A Formal Theory of Inductive Inference by Ray Solomonoff (1964) [paper] — Foundational paper on algorithmic probability and universal induction. Basis for AIXI. Online
Universal Artificial Intelligence by Marcus Hutter (2005) [book] — Formal theory of universal agents combining Solomonoff induction and sequential decision theory. (copyrighted)
Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter (1979) [book] — Self-reference, formal systems, and the nature of mind. Mind-altering. (copyrighted)