Israel's ground invasion of Lebanon: What do we know so far?

Here is what we know about Israel's ground invasion of Lebanon so far:

The Israeli military said its forces launched a "targeted and limited" invasion of southern Lebanon late on Monday.
Hezbollah denied on Tuesday that Israeli forces had entered Lebanon.
UN peacekeepers also said there was no Israeli ground incursion in south Lebanon "right now".
An Israeli security source and Hezbollah both said no direct clashes have taken place between the two sides.
The Israeli military on Tuesday ordered residents of more than 20 towns in southern Lebanon to evacuate immediately.