Some kind of animal has been visited my backyard lawn every night for
a few days. It has digged the grass root out over a large portion of
the lawn and I really need to get rid of it. I do not see any tunnel,
so it is probably not a mole. What are the other types of animals that
may have caused my headache?

Racoons may be the culprits - they tear up huge areas of lawn looking for food.

Trapping may work for the young unwary ones, but the older 'cagey' ones may not
succumb. They will also travel long distances to get back to your lawn, so you
may have to ensure that the trip in the cage is a terminal one.