Wasserstein distance is a class of metrics used to measure the distance between two probability distributions defined on a common metric space. Grounded in optimal transport theory, it quantifies the minimum "cost" required to transform one distribution into the other, where cost is typically defined by the distance in the underlying space. This approach provides a geometrically informed comparison between distributions, offering robustness and sensitivity to the structure of the data space, which is particularly valuable in fields like machine learning, image analysis, and topological data analysis.