An automatic manual transmission for a hybrid car provided with an internal combustion engine and with an electrical machine; the automatic manual transmission comprises: a single-clutch mechanical gearbox, which is provided with: only one primary shaft, which is suited to receive a torque from a crankshaft of the internal combustion engine, only one secondary shaft, which is suited to transmit the torque to driving wheels, a plurality of pairs (I, II, III, IV) of gears (16, 17), each of which has a corresponding gear ratio and comprises a primary gear, which is mounted on the primary shaft, and a secondary gear, which is mounted on the secondary shaft and meshes, in a permanent manner, with the primary gear, and a plurality of first servo-assisted locking devices, each of which is mounted on a shaft (14; 15) and is suited to be actuated so as to lock at least one corresponding gear (16; 17) to the shaft (14; 15); a plurality of first actuators, each of which is coupled to a corresponding first locking device, so as to actuate the locking device; a differential gear, which receives the motion from the secondary shaft of the gearbox and transmits the motion to driving wheels; only one clutch, which is interposed between the only one secondary shaft of the gearbox and the differential gear; a second actuator, which is coupled to the clutch, so as to open and close the clutch; the automatic manual transmission is characterised in that it comprises: an auxiliary shaft, which is different and separate from the primary shaft and from the secondary shaft and along which the electrical machine is mounted; a first gear train, which is different and separate from the pairs (I, II, III, IV) of gears (16, 17) of the gearbox and connects a first end of the auxiliary shaft, which is arranged upstream of the electrical machine, to the primary shaft of the gearbox; and a second gear train, which is different and separate from the pairs (I, II, III, IV) of gears (16, 17) of the gearbox and connects a second end of the auxiliary shaft, which is arranged downstream of the electrical machine, to an output shaft of the clutch. a single-clutch mechanical gearbox, which is provided with: only one primary shaft, which is suited to receive a torque from a crankshaft of the internal combustion engine, only one secondary shaft, which is suited to transmit the torque to driving wheels, a plurality of pairs (I, II, III, IV) of gears (16, 17), each of which has a corresponding gear ratio and comprises a primary gear, which is mounted on the primary shaft, and a secondary gear, which is mounted on the secondary shaft and meshes, in a permanent manner, with the primary gear, and a plurality of first servo-assisted locking devices, each of which is mounted on a shaft (14; 15) and is suited to be actuated so as to lock at least one corresponding gear (16; 17) to the shaft (14; 15); a plurality of first actuators, each of which is coupled to a corresponding first locking device, so as to actuate the locking device; a differential gear, which receives the motion from the secondary shaft of the gearbox and transmits the motion to driving wheels; only one clutch, which is interposed between the only one secondary shaft of the gearbox and the differential gear; a second actuator, which is coupled to the clutch, so as to open and close the clutch; the automatic manual transmission is characterised in that it comprises: an auxiliary shaft, which is different and separate from the primary shaft and from the secondary shaft and along which the electrical machine is mounted; a first gear train, which is different and separate from the pairs (I, II, III, IV) of gears (16, 17) of the gearbox and connects a first end of the auxiliary shaft, which is arranged upstream of the electrical machine, to the primary shaft of the gearbox; and a second gear train, which is different and separate from the pairs (I, II, III, IV) of gears (16, 17) of the gearbox and connects a second end of the auxiliary shaft, which is arranged downstream of the electrical machine, to an output shaft of the clutch. an auxiliary shaft, which is different and separate from the primary shaft and from the secondary shaft and along which the electrical machine is mounted; a first gear train, which is different and separate from the pairs (I, II, III, IV) of gears (16, 17) of the gearbox and connects a first end of the auxiliary shaft, which is arranged upstream of the electrical machine, to the primary shaft of the gearbox; and a second gear train, which is different and separate from the pairs (I, II, III, IV) of gears (16, 17) of the gearbox and connects a second end of the auxiliary shaft, which is arranged downstream of the electrical machine, to an output shaft of the clutch.