Changes in healthcare systems and the availability of new technologies are having a major impact on patient monitoring systems. A patient monitor provides clinicians with data about a patient's health, alerts them when critical conditions are detected, and allows them to track, adjust, and optimize therapy. This can be a matter of life and death, so the demands on the device technology are very high. The use of patient monitoring is no longer limited to selected areas of the hospital, such as intensive care and the operating room. Patient monitoring is expanding to lower acuity areas such as the ward, to the home and even to lifestyle use cases. This course focuses on respiratory and circulatory monitoring. As monitoring is complex and multidisciplinary, it covers physiology, aspects of clinical use, modern clinical measurements, analysis of acquired signals and their characteristics, and architectures of monitoring and therapeutic systems. In the practical part of the course, students will gain hands-on experience with vital sign measurements, analysis of acquired signals for robust extraction of key parameters, and detection of critical states using animal data. The final part of the course discusses future developments in monitoring systems and the challenges and potential use of emerging technologies in hardware and data science. This course is intended for students of electrical engineering, biomedical engineering, medical engineering sciences, applied physics, and mechanical engineering.