What are the most important events and developments in the recent or not so recent past? Climate change? Pandemics? The internet and mobile communications? Artificial intelligence, globalization, or biodiversity loss? Interestingly, all of these areas involve networks. Not because the underlying systems are necessarily networks, but because we can describe them as networks. Over the past decades, networks have emerged as a universal language that we use to design and analyze complex systems, and network science has created many bridges within complexity and to other disciplines.

This open access textbook offers a modern, integrated introduction to complexity science. Taking perspectives from multiple disciplines and using network science as a unifying thread, it highlights both fundamental ideas and the bridges between them. At its core, the book is about understanding through method. Mathematical tools are developed through simple calculations, often accessible with pen and paper, and are consistently applied to real-world problems. Rather than presenting results in finished form, the text derives them constructively, explaining the reasoning that leads to them.

Refined through more than fifteen years of teaching across diverse audiences and continents, the book combines careful exposition with extensive worked examples and exercises. Its goal is not only to teach existing methods, but to equip readers to develop their own.

A physicist by training, Thilo Gross taught mathematics at the University of Bristol and computer science at UC Davis before becoming Professor of Biodiversity Theory at HIFMB Oldenburg. His research focuses on understanding how simplicity emerges in large, complex systems.