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The book uses a new approach to cluster theory by applying skeletal numbers rather than polyhedral skeletal electron pair theory (PSEPT) or cluster valence electron (CVE) counting approach. Zintl ions and matryoshka clusters may be regarded as being inter-related. The skeletal numbers are easy to use and therefore the categorization of any cluster is rapid. A cluster formula regardless of how complex and formidable it may look like is readily decomposed by skeletal numbers into a single whole number digit and by knowing the number of skeletal elements involved, the cluster is categorized. The categorization is expressed by a simple formula K=CyC[Mx], where y+x=n, the number of skeletal elements in the cluster, y represents the capping or de-capping skeletal elements of the outer shell of the cluster, and x represents the nucleus, the inner shell of the skeletal elements. With this information as a guide, a tentative cluster shape may be predicted. Furthermore, if needed, the cluster valence electrons can easily be calculated and compared with the numerical number of cluster valence electrons calculated using the conventional method.

The introductory section of the book provides examples of a selected method of how the skeletal numbers can be applied to analyze and categorize transition metal carbonyl clusters. It also puts a distinction between the skeletal number (K) of an element and the skeletal linkages (K) of two or more skeletal elements bound together in a cluster. The relationship between the empirical formula, K= ¿ [E-V] and V=18n-2K for transition metal clusters or V= 8n-2K for main group elements is illustrated. The six fundamental equations for calculating cluster valence electrons (CVE) are provided. There are four articles which analyze and categorize clusters using mainly skeletal numbers approach and three others which categorize clusters applying the 4N series approach when the skeletal numbers had not yet been discovered. All in all, the book equips the reader with powerful methods of analyzing and categorizing any cluster from the main group or transition metal elements.