The course includes theory and state-of-the-art of methods and algorithms in Real-Time Embedded Systems. Real-Time Embedded Systems are usually complex and have to be carefully analysed and verified before deploying them. The aim of the course is to show the challenges in analysis and verification of such systems. The course starts with introducing concepts and terminology of Real-Time Embedded Systems. It continues with discussion about Real-Time Operating Systems (RTOS), Scheduling Algorithms, Resource Handling and Synchronization Protocols, Real-Time Communication, Real-Time Scheduling on Multiprocessors, Resource Handling and Synchronization on Multiprocessors.