Definition:Fundamental Group

Definition
Let $\struct {X, x_0}$ be a pointed topological space with base point $x_0$.

The fundamental group $\map {\pi_1} {X, x_0}$ 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 known as
The fundamental group is also known more explicitly as the fundamental homotopy group.

Also see

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