Complexity is not a new issue. In fact, in their day, William of Ockham and René Descartes proposed what can best be described as reductionist methods for dealing with it. Over the course of the twentieth century, a science of complexity has emerged in an ever-increasing number of fields (computer science, artificial intelligence, engineering, among others), and has now become an integral part of everyday life. As a result, everyone is confronted with increasingly complex situations that need to be understood and analyzed from a global perspective, to ensure the sustainability of our common future. Complexities 1 analyzes how complexity is understood and dealt with in the fields of cybersecurity, medicine, mathematics and information. This broad spectrum of disciplines shows that all fields of knowledge are challenged by complexity. The following volume, Complexities 2, examines the social sciences and humanities in relation to complexity.