You are probably reading this book because you have an interesting source of data and you suspect it is not a linear one. Either you positively know it is nonlinear because you have some idea of what is going on in the piece of world that you are observing or you are led to suspect that it is because you have tried linear data analysis and you are unsatisfied with its results.

Linear methods interpret all regular structure in a data set, such as a dominant frequency, through linear correlations (to be defined in Chapter 2 below). This means, in brief, that the intrinsic dynamics of the system are governed by the linear paradigm that small causes lead to small effects. Since linear equations can only lead to exponentially decaying (or growing) or (damped) periodically oscillating solutions, all irregular behaviour of the system has to be attributed to some random external input to the system. Now, chaos theory has taught us that random input is not the only possible source of irregularity in a system's output: nonlinear, chaotic systems can produce very irregular data with purely deterministic equations of motion in an autonomous way, i.e., without time dependent inputs. Of course, a system which has both, nonlinearity and random input, will most likely produce irregular data as well.

Although we have not yet introduced the tools we need to make quantitative statements, let us look at a few examples of real data sets. They represent very different problems of data analysis where one could profit from reading this book since a treatment with linear methods alone would be inappropriate.