Yes, Trump will build his border wall. Most of it is already built.
November 21, 2016 The Washington Post
Peter Andreas in The Washington Post, "Critics were as dismissive of Trump’s wall as they were of Trump as a presidential candidate. The wall proposal, they said, was nothing more than a political fantasy. But under President Trump, the wall will not only be for real, but it may be one of his biggest political successes."
Read more on Peter Andreas' research on the U.S.-Mexican border.