A trigger assembly comprising a housing adapted to mount a trigger, hammer and sear therein. The housing has an adjustment feature adapted to fixedly mount the housing within the trigger chamber portion of the firearm. The trigger assembly is particularly conducive for an AR-15 type rifle and the various sear engagement surfaces are adapted to be adjustable irrespective of the various dimensions and tolerances of the underlying firearm. A safety system is employed that adjustably allows proper engagement of the trigger tail to properly engage and disengage the safety mechanism.