= Solution
A <Kleinian group> is a <discrete subgroup> of $\operatorname{PSL}_2(\mathbb C)$, acting by <Möbius transformations> on the <Riemann sphere>, equivalently by orientation-preserving <isometries> of <hyperbolic space> $\mathbb H^3$.
Consider the classes of
$$
A=\begin{pmatrix}1&2\\0&1\end{pmatrix},\qquad B=\begin{pmatrix}1&0\\2&1\end{pmatrix}.
$$
They generate a discrete subgroup because their matrix representatives have integer entries: a sequence of such matrices converging to $I$ or $-I$ is eventually constant. On the real projective line set $X=\{x:|x|>1\}\cup\{\infty\}$ and $Y=\{x:|x|<1\}$. For every nonzero integer $m$,
$$
A^m(x)=x+2m,\qquad B^m(x)=\frac{x}{2mx+1},\qquad A^m(Y)\subset X,\quad B^m(X)\subset Y.
$$
The last inclusion follows from $|2mx+1|\geq2|x|-1>|x|$ when $|x|>1$; also $B^m(\infty)=1/(2m)\in Y$. The <ping-pong lemma> therefore says that the subgroup is the <free product> $\langle A\rangle*\langle B\rangle$. Both generators have infinite order, so
$$
\boxed{\langle A,B\rangle\cong\mathbb Z*\mathbb Z,}
$$
a <free group> on two generators. The ping-pong inclusions ensure that no nonempty reduced word can act as the identity, which is the essential freeness argument.
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