 Complexity science is a new approach or method to science that has arisen over the past few decades to present an alternative paradigm to our traditional methods of scientific inquiry. To give it context, let's start by talking a bit about our traditional approach to scientific research. We can loosely define science as a type of inquiry into the world around us, as opposed to other areas such as art or religion that are based upon aesthetics or revelation. The scientific method of inquiry claims to be based upon empirical data, otherwise known as facts. The beginning of the modern era, approximately 500 years ago, saw the development of a systematic and coherent framework for conducting this scientific inquiry. This framework became most clearly formulated within the work of Sir Isaac Newton, and thus Newtonian physics became an example or paradigm of how modern science should be conducted. The Newtonian paradigm is a whole way of seeing the world that describes phenomena as the product of linear cause and effect interactions between isolated objects that are determined by mathematical laws. This view of things results in a very mechanical vision of the world, sometimes called the Crockwork universe. This paradigm in turn gave rise to a new method of inquiry called reductionism. Reductionism is the process of breaking down complex phenomena into simple components that can be modelled using linear equations, by then reassembling these individual components we can understand the whole system as simply the sum of its individual parts. Having been phenomenally successful within physics, this framework for modern science has gone on over the centuries to be applied to almost all areas of inquiry from biology to engineering and business management, placing it at the heart of our modern understanding of the world. It is only during the 20th century that this approach to science began to be called into question, as the revolution of quantum physics and relativity showed some of its basic assumptions about time and space and causality to be in fact flawed, whilst later in the century chaos theory began to open up a whole new world of non-linear systems. Outside of science, the world had also become very different from the one of Newton, as globalization, information technology and sustainability present us with new challenges of understanding, designing and managing systems that are highly interconnected, interdependent and non-linear, what we now call complex systems. This is where complexity science comes in, to provide us with an alternative scientific method better suited to researching these complex systems, supported by a paradigm that sees the world as a set of interconnected elements, whose interaction give rise to the patterns that we observe in the world around us, as opposed to traditional science that tries to eliminate complexity by studying the individual components of systems in an isolated environment. Complexity science places a greater emphasis upon open systems, that is understanding systems within the complex relations that give them context. Whereas traditional, reductionist science primarily uses linear mathematical models and equations as its theoretical foundations, complexity science uses the concepts of complexity theory, such as self-organization, network theory, adaptation and evolution. This new theoretical framework is combined with new methods such as agent-based modeling, as opposed to describing the phenomena we observe in terms of laws of in terms of laws of nature encoded in equations. Agent-based modeling takes a more bottom-up approach, describing them as the emergent phenomena of local level interactions, of agents that are governed by simple rules. Complexity science studies the complex systems in our world that have previously fallen between the gaps in modern science, such as financial networks, cities, ecosystems and social networks. Studying these large, complex systems typically requires significant amounts of data. Thus, what the microscope, telescope and laboratory were to modern science, computation and data are to complexity science, which relies heavily on computer simulations and analysis of the mass of rich and diverse data that information technology has provided us with. In a time when science has become highly specialized and focused upon extreme scales, complexity science is providing a fresh perspective for refocusing on the everyday world in front of us and helping us to bridge the traditional divides between sciences. In so doing it is helping us expand our scientific body of knowledge to make it richer, more inclusive and proving particularly relevant as a new method for providing the knowledge needed to tackle some of the core challenges we face at the turn of the 21st century.