A transmission includes first and second rotating shafts arranged in parallel and multiple gear sets including gears fixed to the first rotating shaft and rotatable gears rotatably supported on the second rotating shaft. Each gear set includes first and second engagement units engaged with first and second engagement-target portions formed on end surfaces of each rotatable gear and transmitting torque in first and second rotational directions; and a shift mechanism axially and independently moving the first and second engagement units. Each one of the first and second engagement units has a slanted portion allowing the engagement unit to withdraw from the rotatable gear when the other one of the engagement units is disengaged and torque transmitted in a corresponding direction is input. Each one of the first and second engagement unit of each gear set moves integrally with the other one of the engagement units of an adjacent gear set.