\begin{definition}[Definition:Coset Space/Left Coset Space]
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
The '''left coset space (of $G$ modulo $H$)''' is the quotient set of $G$ by left congruence modulo $H$, denoted $G / H^l$.
It is the set of all the left cosets of $H$ in $G$.
{{refactor|This last sentence should probably be extracted into a separate result (i.e. that the quotient set of $G$ w.r.t. congruence modulo $H$ is the same as the set of all cosets of $H$ in $G$), or as an alternative definition and then show the equivalence of definitions. Do not forget to do the dual work for right cosets|level = medium}}
\end{definition}