Data center power system design has traditionally emphasized efficiency and reliability. With rapid growth in both scale and number of data centers, stability is becoming an important concern for power systems inside data centers as well as the grid they connect to. With virtually every watt of electricity processed by power converters at least 2-3 times, data centers have a very high concentration of power electronics, creating the potential for new types of instability that have challenged the development of renewable energy and power grids in recent years. Depending on the nature and extent, an instability event may shut down an entire data center or parts of it due to protective actions or damages to power supplies and other components, making reliability assessment based on normal hardware failure meaningless. This seminar introduces the concept of data center power system stability, reviews possible behavior and consequences of instability, and presents practical methods to analyze and mitigate the problem. Impedance-based frequency-domain models are developed for power supplies and overall data center power systems and used to study system stability. Practical methods to solve typical instability problems and to guarantee stability through the design of power supplies and other components are also presented. The topics are treated in-depth for an intermediate/advanced audience.