A metric space is a set equipped with a function that defines a distance between any two points in the set. This function, called a metric, must satisfy specific properties: it must be non-negative, equal to zero only when the two points are the same, symmetric, and satisfy the triangle inequality. In a metric space, the concept of "closeness" can be rigorously defined, allowing for the exploration of various mathematical concepts such as continuity, convergence, and compactness. Metric spaces are foundational in topology and are widely used in various fields of mathematics and applied sciences.