We are living in an ever more complex world, an epoch where human actions can accordingly acquire far-reaching potentialities. Complex and adaptive dynamical systems are ubiquitous in the world surrounding us and require us to adapt to new realities and the way of dealing with them. This primer has been developed with the aim of conveying a wide range of "commons-sense" knowledge in the field of quantitative complex system science at an introductory level, providing an entry point to this both fascinating and vitally important subject. The approach is modular and phenomenology driven. Examples of emerging phenomena of generic importance treated in this book are. 'The small world phenomenon in social and scale-free networks. Phase transitions and self-organized criticality in adaptive systems. Life at the edge of chaos and coevolutionary avalanches resulting from the unfolding of all living. The concept of living dynamical systems and emotional diffusive control within cognitive system theory. This second edition adds a new chapter on quantifying/measuring complexity in given systems, together with an introduction to information theory, has an expanded exercises and solutions section, and contains both revised and additional subsections. --Book Jacket.