He made his debut with Hillary Clinton at a rally in South Florida, an occasion that gave him a chance to show off his Spanish.

He introduced himself to the nation with a prime-time address at the Democratic convention, inspiring numerous dad jokes along the way.

Then he joined Mrs. Clinton on a three-day bus tour — though no one would have mistaken him for the marquee attraction — and his voice grew noticeably hoarse.

Now, Senator Tim Kaine of Virginia is hitting the campaign trail as a solo act.

Ten days after Mrs. Clinton selected Mr. Kaine to be her running mate, his introduction to voters enters a new phase on Monday as he begins to hold his own events.