Complexity theory may refer to:
the study of any complex system
chaos theory
Computational complexity theory, a field in theoretical computer science and mathematics dealing with the resources required during computation to solve a given problem
the theoretical treatment of Kolmogorov complexity of a string studied in algorithmic information theory by identifying the length of the shortest binary program which can output that string
the application of complexity theory to organizations, which has been influential in strategic management and organizational studies; this area is sometimes referred to as complexity strategy or the study of complex adaptive organizations.
The study of complex systems is bringing new vitality to many areas of science where a more typical reductionist strategy has fallen short. Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines including neuroscience, meteorology, chemistry, physics, computer science, artificial life, evolutionary computation, economics, earthquake prediction, heart cell synchronisation, immune systems, reaction-diffusion systems, molecular biology, epilepsy and inquiries into the nature of living cells themselves. In these endeavours, scientists often seek simple non-linear coupling rules which lead to complex phenomena (rather than describe - see above), but this need not be the case. Human societies (and probably human brains) are complex systems in which neither the components nor the couplings are simple. Nevertheless, they exhibit many of the hallmarks of complex systems.
Traditionally, engineering has striven to keep its systems linear, because that makes them simpler to build and to predict. However, many physical systems (for example lasers) are inherently "complex systems" in terms of the definition above, and engineering practice must now include elements of complex systems research.
Information theory applies well to the complex adaptive systems, CAS, through the concepts of object oriented design.