This book introduces the mathematical foundations of distributionally robust optimization (DRO) for decision-making problems with ambiguous uncertainties and applies them to tackle the critical challenge of energy storage sizing in renewable-integrated power systems, providing readers with an efficient and reliable approach to analyze and design real-world energy systems with uncertainties. Covering a diverse range of topics, this book starts by exploring the necessity for energy storage in evolving power systems and examining the benefits of employing distributionally robust optimization. Subsequently, the cutting-edge mathematical theory of distributionally robust optimization is presented, including both the general theory and moment-based, KL-divergence, and Wasserstein-metric distributionally robust optimization theories. The techniques are then applied to various practical energy storage sizing scenarios, such as stand-alone microgrids, large-scale renewable power plants, bulk power grids, and multi-carrier energy networks. This book offers clear explanations and accessible guidance to bridge the gap between advanced optimization methods and industrial applications. Its interdisciplinary scope makes the book appealing to researchers, graduate students, and industry professionals working in electrical engineering and operations research, catering to both beginners and experts.