In three-dimensional spacetime, the Einstein equations imply that source-free regions are flat. This means that localized sources can only affect the global geometry, not the local structure. The authors discuss the effects of these sources, particularly those generated by mass and angular momentum. They derive the global $\mathcal{N}$-body geometry both analytically and geometrically, and analyze the angular momentum of moving particles. The paper also explores the linearized approximation and the absence of a Newtonian limit. The authors emphasize that their discussion is focused on ordinary Einstein gravity, rather than topologically massive gravity. The results are significant for understanding the global and topological features of this $(2+1)$-dimensional world, and they suggest that quantization of angular momentum could correspond to quantization of the jumps in the time coordinate.In three-dimensional spacetime, the Einstein equations imply that source-free regions are flat. This means that localized sources can only affect the global geometry, not the local structure. The authors discuss the effects of these sources, particularly those generated by mass and angular momentum. They derive the global $\mathcal{N}$-body geometry both analytically and geometrically, and analyze the angular momentum of moving particles. The paper also explores the linearized approximation and the absence of a Newtonian limit. The authors emphasize that their discussion is focused on ordinary Einstein gravity, rather than topologically massive gravity. The results are significant for understanding the global and topological features of this $(2+1)$-dimensional world, and they suggest that quantization of angular momentum could correspond to quantization of the jumps in the time coordinate.