Google tightened its grip on digital advertising with a push deeper into the mobile world on Monday as it agreed to buy AdMob, the largest mobile advertising network, for $750m in stock.

The deal will give the search company a big foothold in the fastest-growing part of the online advertising business. It will be able to combine its own search ads with AdMob’s network for serving, or delivering, display ads on mobile web pages and in applications that run on mobile phones.