This chapter explains about to enter what is, to many, a mysterious world—the world of factor spaces and the factor based techniques, Principal Component Analysis and Partial Least-Squares (PLS) in latent variables. Many analytical practitioners encounter a serious mental block when attempting to deal with factor spaces. The basis of the mental block is twofold. First, all this talk about abstract vector spaces, eigenvectors, regressions on projections of data onto abstract factors, etc., is like a completely alien language. Second, it is often not clear why we would go through all of the trouble in the first place. PCA will serve as a pre-processing step prior to Inverse least-squares (ILS). The combination of Principal Component Analysis with ILS is called Principal Component Regression, or PCR.