Artificial Intelligence (AI) is the key technology in many of today's novel applications, ranging from banking systems that detect attempted credit card fraud, to telephone systems that understand speech, to software systems that notice when you're having problems and offer appropriate advice. These technologies would not exist today without the sustained federal support of fundamental AI research over the past three decades. This book presents sequential decision theory from a novel algorithmic information theory perspective. While the former is suited for active agents in known environments, the latter is suited for passive prediction in unknown environments.One intention of this book is to excite a broader AI audience about abstract algorithmic information theory concepts, and conversely to inform theorists about exciting applications to AI.