The transmission comprises: a first input shaft carrying first, second and third driving gearwheels associated to odd gears and to a reverse gear; a second input shaft made in the form of a hollow shaft coaxial with the first input shaft and carrying fourth and fifth driving gearwheels associated to even gears; a first friction clutch for coupling the first input shaft to a driving shaft of the vehicle; a second friction clutch for coupling the second input shaft to the driving shaft; a first output shaft arranged parallel to the first and second input shafts and carrying a first idle driven gearwheel meshing with the first driving gearwheel for providing a first gear, a second idle driven gearwheel meshing with the second driving gearwheel for providing a third gear and a third idle driven gearwheel meshing with the fifth driving gearwheel for providing a sixth gear, as well as a first engagement sleeve for selectively engaging the first or the third gear and a second engagement sleeve for engaging the sixth gear; and a second output shaft arranged parallel to the first and second input shafts and carrying a fourth idle driven gearwheel meshing with the first idle driven gearwheel for providing the reverse gear, a fifth idle driven gearwheel meshing with the third driving gearwheel for providing a fifth gear, a sixth idle driven gearwheel meshing with the fourth driving gearwheel for providing a second gear, and a seventh idle driven gearwheel meshing with the fifth driving gearwheel for providing a fourth gear, as well as a third engagement sleeve for selectively engaging the reverse gear or the fifth gear and a fourth engagement sleeve for selectively engaging the second or the fourth gear.