A short primer in cluster science, ideal for a short lecture course for advanced undergraduate students. The book is based on a series of lectures delivered for more than ten years by the authors at undergraduate level, and also introduces topics and ideas discussed in former publications of the authors, e.g. the book ?Introduction to cluster dynamics? (2003). The book aims at covering both the basics of the topic (general concepts, experiment, theory, a concise view of cluster properties) and also up-to-date developments. It can roughly be divided in two parts. By providing a general introduction complemented by experimental and theoretical aspects, the first three chapters introduce basic concepts of cluster science. The second part of the book is devoted to a systematic presentation of free cluster properties, and to a thorough discussion of the impact of clusters in other domains of science. Chapter 4 illustrates various cluster properties on simple cases, thus avoiding difficulties connected to more complex situations such as encountered in deposited or embedded clusters. The following chapters explicitly work out the links between cluster physics and other research areas. This makes the book unique both in terms of fundamental aspects and applications. Chapter 5 addresses in detail the importance of cluster science in the fields of materials science and nanosystems. Ideas introduced in the simpler case of free clusters (chapter 4), are exploited, but the authors now explore how things evolve in the more demanding case of embedded and deposited clusters. Considering clusters as small nanosystems, this chapter also discusses the relation to larger systems relevant in materials and surface science. Finally chapter 6 broadens the discussion still further, by expanding the topic to related research fields. The authors address the interfaces with finite fermion systems, biology, astrophysics and environmental science. The authors are highly respected and international experts in the field of cluster science. Having worked in cluster physics for a very long time, they are in an excellent position to create a successful and popular book on the topic. This concise, yet broad coverage of the field will bemostly used at a student level but will also be valuable to researchers outside the field, who are looking for an introduction to it