Dolan gives you a very thorough and accurate account of this book for amazon. So I will not repeat that type of description of the book. Rather I would like to emphasize the applications of factor analysis. Historically multivariate techniques such as principal components and canonical correaltions were well accepted and non-controversial topics is dimensioanlity reduction of high dimensional multivariate analysis. Factor analysis is another way to go about this but was considered controversial and easily abused by the experts in multivariate analysis including T. W. Anderson. However, factor analysis became the favored technique in psychology (psychometrics) as well as some of the other social sciences. For many years Harman's was the key book to go to for a rigorous treatment of the subject. unlike principal components and canonical correlation which have unique solutions there is not a unique solution to the factor analysis problem and there I think is the reason for the controversy. However, the theory has continued to develop and applications have grown. In my field on clinical trials quality of life instruments are often used and factor analysis is used to identify domains and summarize the responses in a small number of domains (factors). It is also considered an attractive approach because often the researcher can after the fact find a rationale to explain the factors and factor weights (or loadings).
This book is different from most in that it emphasizes applications in the "hard" sciences such as botany, zoology, geology and oceanography. It also addresses the effect of atypical or outlying observations on the analysis, covering robust estimation and the identification of influential observations.