Yearly global mean temperature and ocean levels, daily share prices, and the signals transmitted back to Earth by the Voyager space craft are all examples of sequential observations over time known as time series. This book gives you a step-by-step introduction to analysing time series using the open source software R. Each time series model is motivated with practical applications, and is defined in mathematical notation. Once the model has been introduced it is used to generate synthetic data, using R code, and these generated data are then used to estimate its parameters. This sequence enhances understanding of both the time series model and the R function used to fit the model to data. Finally, the model is used to analyse observed data taken from a practical application. By using R, the whole procedure can be reproduced by the reader. All the data sets used in the book are available on the website http://staff.elena.aut.ac.nz/Paul-Cowpertwait/ts/. The book is written for undergraduate students of mathematics, economics, business and finance, geography, engineering and related disciplines, and postgraduate students who may need to analyse time series as part of their taught programme or their research. Paul Cowpertwait is an associate professor in mathematical sciences (analytics) at Auckland University of Technology with a substantial research record in both the theory and applications of time series and stochastic models. Andrew Metcalfe is an associate professor in the School of Mathematical Sciences at the University of Adelaide, and an author of six statistics text books and numerous research papers. Both authors have extensive experience of teaching time series to students at all levels.