Here we present the weak-lensing results for A1758, which is known to consist of four subclusters undergoing two separate mergers, A1758N and A1758S. Weak-lensing results for A1758N agree with previous weak-lensing results for clusters 1E0657-558 (Bullet cluster) and MACS J0025.4-1222, whose X-ray gas components were found to be largely separated from their clusters' gravitational potentials. A1758N has a geometry that is different from previously published mergers in that one of its X-ray peaks overlays the corresponding gravitational potential and the other X-ray peak is well separated from its cluster's gravitational potential. The weak-lensing mass peaks of the two northern clusters are separated at the 2.5sigma level. We estimate the combined mass of the clusters in A1758N to be (2.2 + or - 0.5) x 10 super(15) M sub(sm circle in circle) and r sub(200) = 2300 sub(-130) super(+100) kpc. We also detect seven strong-lensing candidates, two of which may provide information that would improve the mass measurements of A1758N.