This book holds up very well after 35 years, and is readable and useful today. Most data scientists have encountered the idea of principal component analysis, so I'll explain factor analysis relative to it. Factor analysis considerably extends PCA, by allowing factors which are correlated with each other (and then higher-order factors based on these correlated factors). It also allows for the possbility of explaining only communal variance (that captured by at least two variables) instead of all variance. The third extension is that in factor analysis, the factors or components may be post-rotated after they are extracted and truncated, to re-align them better with the original variables. This book explains all of these techniques and gives considerable empirical wisdom on which should be used when.
One caveat I will offer is that this book is useful only for exploratory factor analysis. Although there is a chapter on confirmatory factor analysis (testing a clearly defined hypothesis about the structure), it is too brief and does not sufficiently explain how the analysis is actually conducted.