The notation "π₁(X, x₀)" represents the fundamental group of a topological space X based at a point x₀. This group captures the idea of loops in X that start and end at x₀, allowing us to study the space's shape and structure. Two loops are considered equivalent if one can be continuously deformed into the other without leaving the space. The fundamental group is an important concept in algebraic topology, as it provides insights into the properties of X. For example, if π₁(X, x₀) is trivial (consists only of the identity element), it indicates that every loop can be shrunk to a point, suggesting that X is simply connected.