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Gaussian Interference Channels introduces both classic and recent capacity theorems for the two-user Gaussian interference channel including both the single-antenna and the multiple-antenna cases. The reader is presented with a comprehensive overview of the single-antenna case. Starting from the basics, including capacity outer bounds and achievable rate region several capacity results for single antenna Gaussian interference channel are described. This section concludes with a full discussion on the capacity region and sum-rate capacity for various types of interference. The more complex multiple-antenna case uses multiple-dimensional signaling that results in new interference states including generally strong, generally noisy and generally mixed interference are introduced to obtain capacity theorems that generalize those for the single-antenna case. Gaussian Interference Channels is essential reading for all researchers and scientists in information theory and communications.