Speech recognition has become a challenging task to create an intelligent recognizer that emulates a human being’s ability in speech perception under all environments. The feature extraction of speech is one of the most import issues in the field of speech recognition. In order to achieve high recognition accuracy, the feature extractor is required to discover salient characteristics suited for classification. In this thesis, feature extraction methods and dimensionality reduction methods for feature space are examined. This thesis is divided in three parts. In the first part, speech recognition techniques are reviewed, and several linear and non-linear dimensionality reduction methods are investigated. In the second part, a new linear and a non-linear dimensionality reduction method are proposed in this thesis. In the last part, a new feature extraction technique for speech recognition is presented.