The Fundamental Group is a concept in algebraic topology that captures the idea of loops in a space. It is defined for a topological space and consists of equivalence classes of loops based at a point, where two loops are considered equivalent if one can be continuously deformed into the other. This group helps in understanding the shape and structure of the space. The Fundamental Group is denoted as π₁(X, x₀), where X is the space and x₀ is the base point. It provides important information about the space's connectivity and can distinguish between different topological spaces. For example, the Fundamental Group of a circle is Z, indicating that loops can wrap around the circle an integer number of times.