The concept of list is very important in functional programming and data structures in computer science. The classical definition of lists was redefined by Jena, Tripathy, and Ghosh (2001) by using the notion of position functions, which is an extension of the concept of count function of multisets and of characteristic function of sets. Several concepts related to lists have been defined from this new angle and properties are proved further in subsequent articles. In this chapter, the authors focus on crisp lists and present all the concepts and properties developed so far. Recently, the functional approach to realization of relational databases and realization of operations on them has been proposed. In this chapter, a list theory-based relational database model using position function approach is designed to illustrate how query processing can be realized for some of the relational algebraic operations. The authors also develop a list theoretic relational algebra (LRA) and realize analysis of Petri nets using this LRA.