Understanding $X_n = \big\{ \text{lattices } Λ < \Bbb R^n: \operatorname{covol} Λ = 1\big\} \cong SL(n, \Bbb Z) \setminus SL(n, \Bbb R)$

Question

$X_n = \big\{ \text{lattices } Λ < \Bbb R^n: \operatorname{covol} Λ = 1\big\} \cong SL(n, \Bbb Z) / \operatorname{SL}(n, \Bbb R)$, with isomorphism given by: $\Bbb Zv_1 + \Bbb Zv_2 + \cdots + \Bbb Zv_n \mapsto SL(n, \Bbb Z)(v_1, \ldots , v_n)^T$

Please help me understand why this is true?

From what I understand, the LHS of the map: $\Bbb Zv_1 + \Bbb Zv_2 + \cdots + \Bbb Zv_n$ represents the lattice. The RHS of the map: $SL(n, \Bbb Z)(v_1, \ldots , v_n)^T$ is the special linear group over the integers? But what is this: $(v_1, \ldots , v_n)^T?$