Stefan Andreev, guest lecturing in MIT's 18.642 Topics in Mathematics with Applications in Finance, lays out Principal Component Analysis as a tool for quantitative finance. He builds the mathematical foundations of PCA from covariance matrices and eigenvectors, then applies the method to the U.S. bond market, showing how a small number of factors, typically level, slope, and curvature, capture most of the variation in yield curve dynamics. Andreev works through the practical obstacles of applying PCA to real market data, including noisy correlations and the instability of estimated factors, and connects the technique to portfolio construction and risk management in markets where instruments are highly correlated. The eighty-three minute session mixes derivation with concrete bond market examples, aimed at students who already have a grounding in linear algebra and probability, and gives a clear picture of how an abstract statistical method becomes a working tool on a trading desk.