CINCINNATI, Ohio—President-elect Donald Trump on Thursday said his administration would usher in a new “Industrial Revolution,” one of numerous promises he made in Cincinnati as he began a nationwide “Thank You” tour following his Nov. 8 election.

Mr. Trump used the 53-minute speech, the first of its kind since he became president-elect, to reflect on his victory but also to outline a number of goals, many of them lofty, for his term as president.

The...