This chapter provides an in-depth exploration of the core metrics of Network Science, with a particular emphasis on manual calculations and step-by-step numerical examples. After a detailed examination of paths and graph density, the chapter moves on to a variety of centrality metrics, including degree centrality, node strength, closeness centrality, and betweenness centrality. The exploration continues into the domain of spectral centrality measures, where concepts such as neighborhood, the Jaccard coefficient, Eigenvector centrality, Katz centrality, and PageRank centrality are thoroughly explained. For each measure, step-by-step calculations are performed, walking the reader through the process of quantifying centrality in a network. Techniques for community detection and the concept of homophily are also covered in detail. Concepts like the E-I homophily index, cosine similarity, structural holes, and entropy are addressed with detailed numerical examples. Practical demonstrations using Stata, R, and Python are applied and shown for each metric discussed. Finally, a case study focusing on innovation networks and patent data provides a tangible application, consolidating the understanding of these metrics within a real-world context.