In this graduate work, the processes of which the autocorrelation function is not absolutely summable are presented. Such processes are called stationary processes with long memory and its application are found in different areas such as climate and hydrology. Definitions and basic results of stationary processes with long memory and two classes of such processes are presented. One of them are fractional ARIMA processes that are the natural expansion of the classical ARIMA processes. The structures of autocorrelation function and spectral density of such processes are presented. Then, statistical estimators are introduced to identify long–range dependence in some time series. These are R/S statistic, log–log correlogram, variance plot, periodogram and Whittle’s approximate ML estimator. The concept of long–range dependence has been introduced in two time series: yearly minimum water level of the Nile River and the global temperature of the northern hemisphere of the Earth.