I received my PhD in Mathematics from Carleton University's School of Mathematics and Statistics, Ottawa (Canada) in 1997. My specialization was the design and analysis of statistical surveys. In the past few years however, I devoted considerable time and energy to the field of inter-rater reliability analysis, in which I published several papers and books (for some of my works in this field see https: //www.researchgate.net/profile/Kilem_Gwet). It is after successfully using principal components to analyze multivariate inter-rater reliability data that I first considered writing this book. I wanted a book that shows step by step how principal components are calculated, what they represent, how they must be used and what their limitations are. These are some of the reasons why I wrote this book, which I hope you will find useful.