Definition:Fundamental Group

Definition
Let $(X, x_0)$ be a pointed topological space with base point $x_0$.

The fundamental group $\pi_1 \left({X, x_0}\right)$ of $X$ at the base 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:Fundamental Group Functor
 * Definition:Homotopy Group
 * Fundamental Group is Independent of Base Point for Path-Connected Space