High pressure fuel pump especially for direct injection internal combustion engine and fuel system and internal combustion engine

A high-pressure fuel pump (10), which is used in particular for direct-injection internal combustion engines, comprises a housing (12) which has a low-pressure inlet (20) and a high-pressure outlet (22). In the housing (12) there is a pump chamber (34) which can be connected to the low-pressure inlet (20) and the high-pressure outlet (22). Furthermore, a control valve (38) is provided, which can connect the pump chamber (34) to the low-pressure inlet (20) and opens toward the low-pressure inlet (20). Also, a check valve (36) with a valve element (76) separate from the control valve (38) is present, which is arranged between the low-pressure inlet (20) and the pump chamber (34) and opens toward the pump chamber (34). In order to simplify the construction of the high-pressure fuel pump (10), it is proposed that the check valve (36) and the control valve (38) be housed in a common valve module (44), which is at least partially inserted into the pump housing (12) and has for the control valve (38) and the check valve (36) a common connection (64) to the low-pressure inlet (20).