SAN FRANCISCO — Facebook built itself into the No. 2 digital advertising platform in the world by analyzing the vast amount of data it had on each of its 1.3 billion users to sell individually targeted ads on its social network.

Now it is going to take those targeted ads to the rest of the Internet, mounting its most direct challenge yet to Google, the leader in digital advertising with nearly one-third of the global market.

On Monday, Facebook will roll out a rebuilt ad platform, called Atlas, that will allow marketers to tap its detailed knowledge of its users to direct ads to those people on thousands of other websites and mobile apps.

“We are bringing all of the people-based marketing functions that marketers are used to doing on Facebook and allowing them to do that across the web,” David Jakubowski, the company’s head of advertising technology, said in an interview.