Time travel is an exciting, scary, and much-sought-after idea that has a lot of problems with it. I don't understand physics, quantum mechanics, or any of that super advanced fancy math few people claim to understand but in reality nobody truly does, but I think I can still list a few problems with it anyway. The principle reason for people wanting to go back in time is to change something that happened in the past, most likely for their benefit, or for some heroic deed they know they could perform because they have all the details on how to perform it.
The doppelgänger problem Imagine you're standing in a room. Nice, white room, good air conditioning, slight scent of carpet, no sounds. Then suddenly a duplicate you appears. If things worked in a way that allowed this to happen you'd probably freak out after you found out it was you from the future. However, I believe there can only be one you at one place in time. So if you went back in time, you'd simply end up like you were at that specific date. Or, you'd end up at the location where the time machine is to be built on, which in itself is its own problem depending on what was there at the time, and if the time machine was underground you're doomed.
The loop problem An event occurs in the past that makes you in the present time want to change it. You hop in your time machine, go back in time, fix the problem, then hop back. The problem is once you fix the problem you eliminate what made you go back in time to change it, thus undoing everything. You've got to be beyond time itself to do something like that, and nobody is that way. So a trip to the past wouldn't allow you to change a thing, except maybe have more knowledge about past things when you return to the present.
Greed It's been well-illustrated in the second Back To The Future movie how greed will come in a big way if time travel becomes possible. Granted, you probably won't be able to change anything, but you can still go look up unclaimed lottery numbers for the next ten years after the date you came from, and rule the world. It's scary, and it's going to happen if time travel is invented. You and I both know that if you had the chance to do that you would.
Again, I have no clear understanding of all this stuff, but those are some major problems I can think of right now.