The chapter "Spatial Networks" by Marc Barthélemy discusses the importance of spatial constraints in network structures and their impact on various processes. Spatial networks, where nodes and edges are embedded in space, are prevalent in many real-world systems such as transportation networks, social networks, and neural networks. The cost associated with edge length significantly affects the topology of these networks, leading to unique characteristics and behaviors. The chapter begins by introducing the concept of spatial networks and their relevance in various fields, including urbanism and epidemiology. It reviews the current understanding of how spatial constraints influence network structure and properties, highlighting recent empirical observations and models of spatial networks. Key topics include: 1. **Characterizing Spatial Networks**: The chapter covers methods to characterize spatial networks, including planar networks and the use of tools like Voronoi tessellations and spectral graph theory. 2. **Empirical Observations**: It discusses the properties of real-world spatial networks, such as transportation networks, infrastructure networks, mobility networks, and neural networks. 3. **Models of Spatial Networks**: The chapter reviews important models of spatial network formation, including random geometric graphs, spatial generalizations of Erdős-Rényi and Watts-Strogatz models, and growing spatial networks. 4. **Processes on Spatial Networks**: Various processes on spatial networks are discussed, such as phase transitions, random walks, synchronization, navigation, resilience, and disease spread. The chapter emphasizes the importance of spatial constraints in shaping network structures and their implications for understanding and modeling complex systems. It also highlights the need for further research to fully understand the effects of space on network properties and processes.The chapter "Spatial Networks" by Marc Barthélemy discusses the importance of spatial constraints in network structures and their impact on various processes. Spatial networks, where nodes and edges are embedded in space, are prevalent in many real-world systems such as transportation networks, social networks, and neural networks. The cost associated with edge length significantly affects the topology of these networks, leading to unique characteristics and behaviors. The chapter begins by introducing the concept of spatial networks and their relevance in various fields, including urbanism and epidemiology. It reviews the current understanding of how spatial constraints influence network structure and properties, highlighting recent empirical observations and models of spatial networks. Key topics include: 1. **Characterizing Spatial Networks**: The chapter covers methods to characterize spatial networks, including planar networks and the use of tools like Voronoi tessellations and spectral graph theory. 2. **Empirical Observations**: It discusses the properties of real-world spatial networks, such as transportation networks, infrastructure networks, mobility networks, and neural networks. 3. **Models of Spatial Networks**: The chapter reviews important models of spatial network formation, including random geometric graphs, spatial generalizations of Erdős-Rényi and Watts-Strogatz models, and growing spatial networks. 4. **Processes on Spatial Networks**: Various processes on spatial networks are discussed, such as phase transitions, random walks, synchronization, navigation, resilience, and disease spread. The chapter emphasizes the importance of spatial constraints in shaping network structures and their implications for understanding and modeling complex systems. It also highlights the need for further research to fully understand the effects of space on network properties and processes.