Many real-life systems are dynamic, evolving, and intertwined. Examples of such systems displaying 'complexity', can be found in a wide variety of contexts ranging from economics to biology, to the environmental and physical sciences. The study of complex systems involves analysis and interpretation of vast quantities of data, which necessitates the application of many classical and modern tools and techniques from statistics, network science, Machine Learning, and agent-based modelling. Drawing from the latest research, this self-contained and pedagogical text describes some of the most important and widely used methods, emphasising both empirical and theoretical approaches. More broadly, this book provides an accessible guide to a data-driven toolkit for scientists, engineers, and social scientists who require effective analysis of large quantities of data, whether that be related to social networks, financial markets, economies or other types of complex systems.In order to develop the empirical apparatus, we first provide an introduction to probability and statistics, covering both classical and Bayesian statistics (Chapter 2). We go through a discussion of the classical approach to probability and develop the concept of statistical estimation and hypothesis testing, leading to a discussion of Bayesian models. Then we discuss time series models to analyze evolving systems (Chapter 3). In particular, we develop ideas to model stationary and non-stationary systems. Additionally, we review some ideas from financial econometrics that have proved to be very useful for modeling time-varying conditional second moment: that is, volatility. In the next part of the book, we review Machine Learning techniques emphasizing numerical, spectral, and statistical approaches to Machine Learning (Chapter 4). Then we discuss network theory as a useful way to think about interconnected systems (Chapter 5). These four components constitute the building blocks of the Data Science approaches to complex systems.

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