Total unimodularity is a property of matrices where every square submatrix possesses a determinant value of 0, +1, or -1. This concept is central to the study of combinatorial optimization and linear programming, as it guarantees that basic feasible solutions to linear programs defined by totally unimodular constraint matrices are integral, provided the right-hand side vector is integral. Research in this area investigates the structural characteristics of matrices that satisfy this property, establishes connections to underlying combinatorial structures such as graphs (e.g., the incidence matrix of a graph is totally unimodular if and only if the graph is bipartite), and develops methods for testing total unimodularity and exploiting its implications for efficient algorithm design in various optimization problems.