Chapter 40 Non linear dynamical systems: Instability and chaos in economics This chapter aims to (1) set enough of the mathematics of dynamical systems from the perspective of chaos theory so that the endogenous emergence of chaotic dynamics and other highly complex dynamics are understood (ii) measures of instability and complexity are explained (iii) how one tests for the presence of chaos and other complex nonlinear dynamics in time series data is discussed; and (iv) how these concepts have been applied in economics is explained. The chapter focuses on discussing the fabric and unity of this subject from the point of view of economic theory and econometrics. Basic mathematics has been developed so that ideas and the notion of chaotic dynamics are defined precisely. In computer science there is a great deal of interest in the properties of random number generators. Measures that are designed to detect chaos can also be used to test random number generators. It raises the issue of what criteria should be used in judging whether or not finite length sequences are random. In statistical hypothesis testing certain measures that are used to detect chaotic dynamics have been used to test for stochastic stationarity and independence.