Space-time adaptive processing (STAP) is a technology for advanced radar systems that allows for significant performance enhancements over conventional approaches. Based on a course taught in industry, government and academia, this is a practical introduction to STAP concepts and methods, placing emphasis on implementation in real-world systems. It addresses the needs of radar engineers who are seeking to apply effective STAP techniques to their systems, and can also be used as a reference by non-radar specialists with an interest in the signal processing applications of STAP. The authors aim to explain critical topics in a manner that should be understandable to anyone with a basic background in radar and signal processing.