We present a weak-lensing and dynamical study of the complex cluster Abell 1758 (A1758, {bar}z=0.278) supported by hydrodynamical simulations. This cluster is composed of two main structures called A1758N and A1758S. The northern structure is composed of A1758NW and A1758NE, with lensing determined masses of 7.90_-1.55_^+1.89^x10^14^M_{sun}_ and 5.49_-1.33_^+1.67^x10^14^M_{sun}_, respectively. They show a remarkable feature: while in A1758NW, there is a spatial agreement among weak-lensing mass distribution, intracluster medium and its brightest cluster galaxy (BCG), in A1758NE, the X-ray peak is located 96_-15_^+14^ arcsec away from the mass peak and BCG positions. Given the detachment between gas and mass, we could use the local surface mass density to estimate an upper limit for the dark matter self-interaction cross-section: {sigma}/m<5.83cm^2^/g. Combining our velocity data with hydrodynamical simulations, we have shown that A1758 NW and NE had their closest approach 0.27Gyr ago and their merger axis is 21+/-12{deg} from the plane of the sky. In the A1758S system, we have measured a total mass of 4.96_-1.19_^+1.08^x10^14^M_{sun}_ and, using radial velocity data, we found that the main merger axis is located at 70+/-4{deg} from the plane of the sky, therefore closest to the line of sight.