This book is an introduction to partial words. These combinatorial objects are an extension of the usual words--except that they have gaps or holes--and they have application in bioinformatics and DNA computing. The holes in partial words change the dynamic considerably, and the focus of the book is on proving results that parallel known results for words, in particular on issues of periodicity, primitivity, and codes.

Chapter 1 covers the preliminaries on partial words. The progress is at a reasonable pace for undergraduates, and the exposition includes many helpful examples. Chapter 2 continues the preliminaries, introducing the concepts of conjugacy and commutativity.

Chapter 3 begins the development of more complex ideas. Its focus is on periodicity--in particular a theorem of Fine and Wilf that states that if a word has periods p and q and length at least p + q - gcd(p,q), then it also has period gcd(p,q). The theorem of Fine and Wilf applies to words; the goal of chapter 3 is to present the research of its extension to partial words. This is done on a case-by-case basis.

Chapter 4 continues the periodicity theme, again extending a theorem about words to an analogue for partial words. In this case, the theorem in question is the critical factorization theorem. Chapter 5 is the final chapter on periodicity, and deals with Guibas and Odlyzko’s theorem for words that states that for any word there is a binary word of the same length and with the same periods. Again, the objective of this chapter is to derive similar results on partial words, although in this case only for the case of 0 or 1 holes.

Chapter 6 begins the study of primitivity. Primitivity means that a partial word is not part of a larger word in a certain sense, that is, the partial word u is primitive if there is no word v with u contained in some nontrivial power of v. The chapter considers a linear-time algorithm to test primitivity, and derives formulas for counting both primitive words and primitive partial words of various types.

Chapter 7 explores unbordered partial words. An unbordered partial word is one that is not bounded on each side: u is unbordered if no nonempty words, x, v, and w exist with u contained in xv and u contained in wx. This chapter explores prefixes, periods, and critical factorizations in this context.

Chapters 8 and 9 extend the idea of codes for words to pcodes for partial words, and develop a detailed theory. In particular, two algorithms are given that test if a set of partial words has the pcode property. The first parallels that of Sardinas and Patterson for words; the second parallels that of Head and Weber for words.

The last section of the book explores a number of specialist topics. Chapter 10 looks at equations on partial words; in particular, it considers when powers of partial words are compatible with one another--that is, whether each is contained inside a larger partial word. Chapter 11 covers correlations of partial words, and chapter 12 concerns unavoidable sets of partial words.

The book is a thorough introduction to the topic that starts at a basic level and proceeds at a manageable pace. There are numerous examples and plenty of exercises, with some solutions given at the end. Programming exercises are also featured, which helps to make the book suitable for computer science students as well as mathematics students. The book would be suitable for an advanced undergraduate course, a graduate course, or for a researcher already familiar with words, but who would like to learn about the parallel world of partial words, although it remains a niche topic. Blanchet-Sadri does mention the usefulness of the topic in bioinformatics and DNA computing; however, it would have improved the book if she had included some concrete examples of this as motivation. Overall, it is a comprehensive and state-of-the-art read.