Is it possible to make a time machine? If yes, how? If no, why?

We feel that we live in a three-dimensional space and the fourth dimension of time. We can move around in the three-dimensional space freely. But feel that we are traveling linearly in time at a constant rate in the same direction (that we call the future).

Einstein’s special theory of relativity leads to Twin’s paradox and simultaneity and such other paradoxical situations- where the relative space-times of two people can change drastically if they relatively travel at speeds comparable to the speed of light. Of course, such high speeds require huge amounts of energy. Mass also becomes heavier at high speeds.

Although very expensive, at least we know how we can travel to the FUTURE- We just have to travel in a spacecraft at high speeds comparable to that of light.
But then, what about traveling to the past?

Also, what about teleportation in the three dimensions- that is, jumping from one point to another without passing through intermediate points? Do you think we need to solve teleportation problem before we can think of solving time-travel?