Definition:Fundamental Group

Definition
Let $X$ be a topological space.

Let $x_0\in X$.

The fundamental group $\pi_1(X, x_0)$ of $X$ at the point $x_0$ is the set of homotopy classes of loops with base point $x_0$ with multiplication of homotopy classes of paths.

Also see

 * Fundamental Group is Group
 * Definition:Homotopy Group
 * Fundamental Group is Independent of Base Point for Path-Connected Space