Time travel in sci-fi literature tends to be approached in two fundamentally different ways, and these two ways correspond to whether time is seen as objective or subjective. The brute force approach, as I’ll call it, ties in with our common sense intuition that time is an objective feature of reality, that it would keep ticking away regardless of whether or not anyone was there to measure it. In this approach, a machine or device is created (or discovered) that somehow allows its user to travel through time in a non-standard way. The mind travel approach, on the other hand, comports with Einsteinian and Kantian considerations about the mind-dependence of time; in it, travelling into the past is shown to be possible through a sort of rigorous mental training or discipline, with no recourse to technology required.
Personally I find the mind travel approach more compelling, but here I want to touch on and recommend two novels from each camp—and one curious outlier.