The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Trevor Hastie, Robert Tibshirani, and Jerome Friedman, 2009 (Springer) - A widely used textbook that provides a thorough treatment of Principal Component Analysis (PCA), the 'curse of dimensionality,' and various other dimensionality reduction methods, offering a strong statistical basis.
Pattern Recognition and Machine Learning, Christopher Bishop, 2006 (Springer) - A comprehensive textbook detailing Principal Component Analysis (PCA) and a range of other linear and non-linear dimensionality reduction techniques, including their underlying mathematical principles.