In this course, the fundamental and advanced concepts of bio-inspired computing are introduced with a focus on understanding how evolutionary systems are different from other complex systems in nature and society. Biological organisms cope with the demands of their environments using solutions quite unlike the traditional human-engineered approaches to problem solving. Biological systems tend to be adaptive, evolvable, resilient, reactive, and distributed. Bio-inspired computing is a field devoted to tackling complex problems using computational methods modeled after design principles encountered in nature. This course is strongly grounded on the foundations of complex systems science and theoretical biology. It aims to provide an understanding of the distributed architectures of evolving complex systems, and how those can be used to produce artificial intelligence and computational tools, as well as engineering designs, with enhanced robustness, scalability, flexibility and which can interface more effectively with humans. It is a multi-disciplinary field strongly based on biology, physics, complexity, computer science, informatics, cognitive science, robotics, optimization, control, and cybernetics. Bio-inspired computing at the core of modern artificial intelligence, and thus applied throughout science and engineering, but understanding the mechanisms behind resilience, evolvability, and adaptation are essential to tackle the most vexing biomedical and social complexity problems we currently face. Therefore, the course should interest students in various programs.