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Universal Artificial Intelligence. Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental probability distribution is known. Solomonoff’s theory of universal induction formally solves the problem of sequence prediction for unknown distribution. With a formal solution I mean a rigorous mathematically definition, uniquely specifying the solution. I unified both theories and gave strong arguments that the resulting universal AIXI model behaves optimally in any computable environment. I also made some progress towards a computable AI theory. I constructed an algorithm AIXItl, which is superior to any other time t and space l bounded agent. The computation time of AIXItl is of the order t·2l. The constant 2l is still too large to allow a direct implementation. My main focus is on theoretical studies related to the AIXI model and on further reducing the time-complexity of AIXItl down to a point where it runs on todays computers with reasonable computation time. This apporach may be characterized as a mathematical top-down approach to AI.