The grandfather paradox is a paradox of time travel in which inconsistencies emerge through changing the past. The name comes from the paradox's common description as a person who travels to the past and kills their own grandfather, preventing the existence of their father or mother and therefore their own existence. Any inconsistency in past events may be regarded as a grandfather paradox.
The grandfather paradox was described as early as 1931, and even then it was described as "the age-old argument of preventing your birth by killing your grandparents". Early science fiction stories dealing with the paradox are the short story Ancestral Voices by Nathaniel Schachner, published in 1933, and the 1943 book by René Barjavel Future Times Three.
Despite its title, the grandfather paradox does not exclusively regard the impossibility of killing one's own grandfather to prevent one's birth. Rather, the paradox regards any action that alters the past. Another example would be using scientific knowledge to invent a time machine, then going back in time and (whether through murder or otherwise) impeding a scientist's work that would eventually lead to the invention of the time machine. An equivalent paradox is known in philosophy as autoinfanticide, going back in time and killing oneself as a baby.
A variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox", a fairly frequent trope in science fiction, in which the protagonist travels back in time to murder Adolf Hitler before he can instigate World War II. Rather than necessarily physically preventing time travel, the action removes any reason for the travel, along with any knowledge that the reason ever existed, thus removing any point in travelling in time in the first place. Additionally, the consequences of Hitler's existence are so monumental and all-encompassing that for anyone born after the war, it is likely that their birth was influenced in some way by its effects, and thus the lineage aspect of the paradox would directly apply in some way.
Another variant is a parallel universe approach to time travel. When the time traveller kills their grandfather, they are actually killing a parallel universe version of their grandfather, and the time traveller's original universe is unaltered. In other variants, the actions of the time traveller have no effect outside of their own personal experience, as depicted in Alfred Bester's short story The Men Who Murdered Mohammed.