A fundamental group is a concept in topology, a branch of mathematics that studies the properties of space. It captures the idea of loops in a space, specifically how they can be continuously transformed into one another. The fundamental group is denoted as π₁(X, x₀), where X is the space and x₀ is a chosen point in that space. This group helps classify spaces based on their shape and connectivity. For example, a circle has a fundamental group that reflects its loops, while a sphere has a trivial fundamental group, indicating that all loops can be shrunk to a point without leaving the surface.