A nonsimple (complex) system indicates a mix of crucial and non-crucial events, with very different statistical properties. It is the crucial events that determine the efficiency of information exchange between complex networks. For a large class of nonsimple systems, crucial events determine catastrophic failures - from heart attacks to stock market crashes. This interesting book outlines a data processing technique that separates the effects of the crucial from those of the non-crucial events in nonsimple time series extracted from physical, social and living systems. Adopting an informal conversational style, without sacrificing the clarity necessary to explain, the contents will lead the reader through concepts such as fractals, complexity and randomness, self-organized criticality, fractional-order differential equations of motion, and crucial events, always with an eye to helping to interpret what mathematics usually does in the development of new scientific knowledge. Both researchers and novitiate will find Crucial Events useful in learning more about the science of nonsimplicity. Sample Chapter(s) Preface Chapter 1: Information is Fundamental Contents: Preface Information is Fundamental Empirical Information Exchange Nonsimplicity, Dynamics & Information Fractal Living Networks Modeling Uncertainty Information Exchange Theory Detecting Crucial Events Crucial Events in 3 Acts Time Series Information Dynamic Linear Response Theory Quantum Nomenclature Bibliography Index Readership: Students, researchers and individuals interested in learning about the science of nonsimplicity.