This chapter reviews the classical PNs and PNs with extensions that will be used in the rest of this book. The key concepts of PNs are demonstrated through running examples in a biochemical context, such as methane combustion, the central dogma of biology, dimerization, phosphorylation/dephosphorylation, reversible enzymatic reactions, and metabolic networks. For each instance, we elucidate the PN visualization of the underlying issue and detail the “token flow mechanics” that govern its dynamic behavior. We show how random and concurrent occurrences of reactions are modeled, including quantitative aspects of kinetic parameters. In addition, we meticulously outline the process of approximating a discrete PN with its continuous counterpart through the application of the fluidization procedure.