Automatic speech recognition (ASR) is a forefront of technology and research today. The effectiveness of ASR depends upon the accurate and quick classification of phonemes, which are the basic building blocks of speech. To derive such a classifier for phoneme classification in the context of ASR is the subject of my MASc thesis at the University of Waterloo carried out in between April 2011 and July 2012 under the supervision of Professor Fakhreddine Karray. Drawing upon several recent research topics applied to this area, such as discriminative learning and locally adaptive metrics, a novel classifier referred to as the discriminative locally-adaptive nearest centroid classifier (DLANC). DLANC is structurally simple, very quick to train on even very large sets of data, and it also produces very good classification results on standard TIMIT data. This book describes the DLANC classifier in detail, including its background and how it is derived. A detailed comparison between the DLANC classifier and several other existing classifiers for phoneme classification are made on standard TIMIT data. Numerous illustrations and diagrams make many theoretical points easy to understand.