In most decision-making and design situations, simultaneously satisfying multiple goals is a trial and error process, and is often inefficient. This trend occurs not only in science and engineering, but also in any discipline involving different people with different intentions, or a single decision-maker with more than one target. Although modeling interactive scenarios between people or groups has long been a topic of the social sciences, the process of systematically optimizing a collection of functions is a relatively new focus within the field of engineering. This process is called multi-objective optimization (MOO). This text presents a comprehensive review of MOO methods with an eye towards engineering applications. This provides not only in a lucid synopsis of theory but also a thorough users guide with ready-to-use formulas and mathematical details. The text can be used as a practical tool for engineering analysts and researchers, as well as for those working with operations research and mathematical systems. It can also serve as an advanced level graduate text, taking students from basic concepts, to mathematical fundamentals, through more advanced methods.