The aim of this traineeship is to design an L1 adaptive controller for a ship autopilot in combination with rudder roll damping. Rudder roll damping means that the rudder of the ship is used to reduce wave induced roll motions of the ship. L1 adaptive control theory is a new adaptive control architecture which decouples estimation (adaptation) from control (robustness), and with that allows for arbitrary fast adaptation. L1 adaptive control is first used to control the heading of a ship. A simple one degree of freedom model is used with a non-linear steering characteristic. The adaptive controller is used to estimate this nonlinearity. The designed adaptive autopilot is then used on a more complex four degree of freedom model.This used benchmark ship model is a 360 ton naval vessel. The L1 adaptive control theory is also used to design a controller which uses the rudder to dampout roll motion of the ship. A model which only contains the equations of motion in roll was used for this. Finally the autopilot is combined with roll damping to get a controller which combines rollreduction with low heading interference