Two characteristic features of Newtonian gravitational n-body problem are its symmetries and its singularities. For the planar three-body problem there symmetries of translation and rotation in the plane and singularities due to collisions of two or of all three bodies. I will describe a way to carry out the symplectic reduction by the the symmetries, ``regularize'' all three binary collisions and blow-up the triple collision to obtain a Hamiltonian system of three degrees of freedom. The reduced phase space is the cotangent bundle of $R^+\times S^2$