Long memory time series are characterized by a strong dependence between distant events. This book introduces into the theory and foundations of univariate time series analysis with a focus on long memory and fractional integration, which are embedded into the general framework. After an introduction, the book presents the general theory of time series, including some issues that are not treated in other books on time series, such as ergodicity, persistence versus memory, asymptotic properties and Whittle estimation. Further chapters address the general functional central limit theory, parametric and semiparametric estimation of the long memory parameter, and locally optimal tests. This book is intended for first year PhD students, researchers and practitioners in statistics, econometrics and any application area that uses time series over a long period.