Self-adaptive systems choose adaptations to perform on a running system. Typically, the self-adaptive system must choose the "best" adaptation to perform in a given circumstance from a set of adaptations that may apply. Utility functions are typically used to encode some measure of goodness or badness the result of choosing a particular adaptation. Within the area of utility theory, there are a set of theories that could be used to help choose the best adaptation, that vary in the assumptions and requirements made about the system, the environment, and the business context of use. By understanding some of the formalities and advanced concepts in Utility Theory, engineers and administrators of self-adaptive systems can create more effective utility functions for their purposes, enable new forms of analysis, and potentially move into new frontiers in self-adaptive systems. In this report, we survey some of the more interesting topics in Utility Theory relevant to self-adaptive systems include objective and subjective expected utility, stochastic and fuzzy utility, and changing and state dependent utility functions.

31 pages

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