Principal component analysis (PCA) is a multivariate technique designed to to reduce highdimensional problems to a lowerdimensional problems. The basic idea is that only axes along which data points have high variance are considered, and the others are discarded. Frankly, if you don't already know what principal component analysis is, you probably don't need a dedicated book. However, if you use or are planning to use principal component analysis, there are many subtle issues that can arise. You will save a lot of time by becoming familiar with those issues from a book rather than dealing (or failing to deal) with them yourself.
Recommended Books

Principal Component Analysis
I.T. Jolliffe
Key Topics
 Biplots
 Canonical Correlation Analysis
 Factor Analysis
 Functional PCA
 Generalizations and Adaptations of Principal Component Analysis
 Geometry of Principal Components
 Interpretation of Principal Components
 Interpreting Principal Components
 Outlier Detection
 Population Principal Components
 Principal Component Analysis for Time Series
 Principal Component Analysis for nonGaussian Data
 Principal Component Regression
 Principal Component Subset Selection
 Principal Components Used with Other Multivariate Techniques
 Projection Pursuit
 Robust Estimation
 Rotation of Principal Components
 Sample Principal Components
Description
We're not exaggerating when we say this is one of the best applied statistics books. There are a surprisingly large number of good books on principal component analysis given that it is a somewhat niche technique, but unfortunately for them they must all compete with this book. The mathematical introduction is succinct and precise, the coverage of practical issues is exhaustive in our experience (we found it somewhat frustrating to find our own supposed insights already in print!), and there many useful extensions of principal component analysis presented. The major drawbacks of this book are that there are no code examples or exercises. It's pretty easy to follow along though as PCA packages are common. You will just need some appropriate data (any tabular data with continuous columns will work for most of the book).