Discrete subgroups of Lie groups other than Lattices

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I know a lattice is a discrete group of $G$ which is of finite covolume. I am just curious to know examples of discrete subgroups of $SL_2(\mathbb{R})$ or in particular $SL_n(\mathbb{R})$ other than lattices which are important in literature. I am also curious to know whether there are some famous (i.e studied rigorously in many contexts)discrete subgroups of $PSL_2(\mathbb{C})$ in literature other than lattices?