If there’s an introductory book on complexity theory, Linked: How Everything Is Connected to Everything Else by Albert-László Barabási would be it. Its layman approach to unlocking the complexity behind the theory is illustrated with familiar examples like

the topology of web pages (where the nodes are individual web pages and the links are hyper-links), the collaborative network of Hollywood actors (where the nodes actors and the links are co-stars in the same movie), the power grid of the western United States (where the nodes are generators, transformers, and substations and the links are power transmission lines), and the peer-reviewed scientific literature (where the nodes are publications and the links are citations).(Source: Wolfram MathWorld)

The book revolves around the idea of scale-free network. Social networks, the Internet, even the economy may be seen from a different perspective using this concept. The author argued that if you strip complexity to its parts, you would come up with its skeleton which is networks. The nodes and links that make up the network comprise the structure of complexity.

The author adds:

The goal before us is to understand complexity. To achieve that, we must move beyond structure and topology and start focusing on the dynamics that take place along the links. Networks are only the skeleton of complexity, the highways for the various processes that make our world hum.

Btw, this is not to say that this is THE only way to understand complexity. It’s only a part in our toolset. Now, we have the topology map at our disposal. The tricky part is mapping the interaction of its parts.