Relational database systems have evolved significantly since their incep- tion over 30 years ago. New applications are now more complex than ever, and tuning a production system for performance has become a critical yet time-consuming activity. Due to the increasing complexity in both application workloads and query engines, even experienced database administrators (or DBAs) cannot fully understand the ramifications of tuning decisions through- out the whole system. As a consequence, the industry began providing auto- mated tuning tools that systematically explore the space of alternatives and guide DBAs. A critical element of such tuning is physical database design, because the choice of physical structures—such as indexes—has a significant impact on the performance of the database system. In this book we present a detailed overview of the fundamental ideas and algorithms to automatically recommend changes to the physical design of a database system.