Changes in health care systems and availability of new technologies have a large impact on patient monitoring systems. The use of patient monitoring is not limited anymore to selected areas in the hospital like the intensive care and operating room but also spreads out towards lower acuity areas like the ward, to the home and even to lifestyle use cases. In this course the focus is on monitoring of respiration and circulation. The relevant physiology and models of respiratory and circulatory body systems are discussed, followed by lectures on modern clinical measurements, signals, waveforms and features, modern monitor systems, therapeutic devices and clinical use. In the last part of the course future developments in monitoring systems and the potential use of emerging technologies in hardware and data science are discussed. This course on patient monitoring is intended for students in applied physics, electrical engineering, mechanical engineering and medical engineering sciences.