Time travel is, of course, the field of traveling through time. It is technically being undertaken by nearly everyone at every given moment, as they are usually moving forward through time (so to speak) but going backwards is the real challenge. Several time machines have been invented for exactly this purpose.
The major problem with time travel, or really, a major problem with time travel, since new problems are being invented at an alarming rate by time travellers everywhere all over history, is, or will be, or was - depending on whether your civilisation has invented time travel, is yet to discover its particular thrills and disappointments, or has already moved on to invent magic and dragon-powered central heating - this:
So many people have now led so many versions of their own lives that it has created a whole new branch of psychological analysis, and a correspondingly large shelf space in bookstores for the associated self-help books, to deal with the particularly prevalent forms of self-envy that come from being unsure if the life one is currently leading is the best, or merely the second-best, life that one could be leading. Indeed, Time Travelers Anonymous has supplanted the formerly well-attended Billionaires Anonymous groups because although it had, of course, become frighteningly commonplace for literally everyone who entered the mid-week lottery to win first prize, the inflation rate would inevitably jump to a thousand percent overnight, and the going rate for a loaf of bread would soon equal, say, two small luxury yachts and a diamond-encrusted miniature purebred poodle's necklace, give or take the poodle.
One of the other major problems encountered in time travel is not that of accidentally becoming your own father or mother. There is no problem involved in becoming your own father or mother that a broadminded and well-adjusted family can't cope with. There is also no problem about changing the course of history - the course of history does not change easily because it all fits together like a jigsaw. All the important changes have usually happened before the things they were supposed to change and it all sorts itself out in the end. When they do change, usually the change is worse and then has to be undone somehow, but that's simple enough.
The really major problem of time travel, however, is quite simply one of grammar, and the main work to consult in this matter is Dr. Dan Streetmentioner's Time Traveler's Handbook of 1001 Tense Formations.