This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School "Galois Theory of Difference Equations" in Santa Marta, Columbia, July 23-August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.

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Charlotte Hardouin and Jacques Sauloy, Institut de Mathematiques de Toulouse, France. Michael F. Singer, North Carolina State University, Raleigh, NC, USA.

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