There's something irresistible about the concept of time travel; it can seduce even those who are sternly resistant to the rest of the sci-fi genre.
And the idea of being able to revisit - and perhaps change - key moments in Earth's history is especially compelling. I think most people have encountered one or two favourite stories of this type, and almost all writers have surely tried to write one at some point.
One such that particularly lodged in my brain when I was a kid (I think it might have been one of Ray Bradbury's, but I'm not sure; can't remember the title now) was about a company running historical tours into the past. One of their most popular destinations was the crucifixion of Jesus. The tourists had to be very carefully briefed to fit in with the Judaean crowds, not attract attention to themselves - not do anything that might change the outcome of events. So, when the moment came, the group all chanted 'Free Barabbas!', as they had been told to do. Only a few of them noticed that they were the only people doing so.
Of course, if you could travel back in time to attempt an intervention that might change the course of human history for the better, the most obvious choice for most people would be to assassinate Adolf Hitler before he comes to power in Germany. So, unoriginal fellow that I so often am, I wrote a story about that when I was in my early teens.
I was interested in the notion of events being fixed, of it proving to be impossible for time travellers to effect any changes in history. In some stories I've read, this effect is realised by mysterious laws of physics - invisible force fields or whatever that thwart the protagonist's action at the critical moment. I preferred to focus on the mundane frustrations of daily life, to suggest that the ordinary ebb and flow of events might more effectively obstruct my hero's plans. And so I had events like the breakdown of a tram, a sudden rainstorm, and the last-minute cancellation of a speaking engagement keeping my would-be assassin from his planned encounters with Hitler. I even toyed with - but didn't ultimately use - the idea of him having a revolver that he'd acquired for the purpose fail to work. (I was playing with the physics-will-thwart-you device, making it seem that the gun had uaccountably refused to fire because of some strange Law of Time; but I then planned to reveal that there was in fact a straightforward explanation - he'd bought the gun from a pawnbroker [being unable to bring any weapons with him through the time-portal], who, fearing that he planned to commit suicide with it, had deliberately sold him one with a faulty firing-pin.)
And for a final mess-with-your-mind twist.... my hero was disheartened, realised that it was seemingly impossible for him to complete the mission he had set himself, and was preparing to return to his own time. Walking down the streets of 1920s Munich one last time, he sees a man just ahead of him distractedly step into the road directly in front of a bus (or a tram; I suspect they had trams - but I never did the research to check this). Instinctively, he grabs the man and pulls him back to safety. The man loses balance and falls on top of him. As they pick themselves up, the hero finds himself finally face to face with....
Too obvious? Well, I was only 13 or 14; give me a break.
On the other side of the Allies/Axis divide, I was also intrigued as to how the untimely death of Winston Churchill might have altered history (I was very probably influenced by Jack Higgins' The Eagle Has Landed, which came out when I was on the cusp of my teens). There does seem to be a powerful argument that he was the main force in the Cabinet resisting Nazi peace overtures, and that without him Britain might have withdrawn from the War - and left Hitler secure in his European conquests, perhaps even able to make a success of his invasion of Russia and to resist involving himself in the later US-Japan war.
My seed idea here was wondering what is the smallest event that can lead to a major change in the course of history - the concept of The Butterfly Effect. I looked down to the molecular level, and decided that there must be a point where, a point where... something like the combustion process inside a car's engine is at a critical threshold, a whisker away from failing. In one reality, a car engine stalls; in another, it shudders, but just manages to keep turning over. What might flow from that?
I didn't quite have the story structure worked out to my satisfaction. It was difficult to incorporate this idea of history turning on the smallest of events inside a car's engine with the adventure story I wanted to write. What I came up with was an alternating chapter structure with two essentially unrelated stories - the connection between them only gradually emerging towards the end.
In the first story strand, an underground group is planning a terrorist campaign against an oppressive government. It is slowly revealed that this is 1970s Britain, under the sway of a Fascist party aligned with the Third Reich which still rules Germany and most of Europe.
The second story strand is set thirty-odd years earlier, in London at the outset of WWII. A car that nearly stalls - but doesn't - speeds impatiently away from a traffic light and knocks over a pedestrian a few moments later. The man survives, but suffers serious injuries and temporary amnesia. Police trying to establish his identity find some odd discrepancies in his personal history, and call in a military investigator - who eventually discovers that the man is a German secret agent with a mission to assassinate Churchill.
Hence, we come to a final realisation that the main story is happening in a Europe still controlled by the Nazis because, if that car had stalled on a foggy London street in 1940, the German agent would have fulfilled his mission... and removed Britain from the War.