The rains that postponed many of the scheduled matches on Sunday gave way to sunshine Monday and Olympic organizers filled up the outer courts to try to get back on track.
American Andy Roddick, whose match was postponed Sunday, reached the second round with a 7-5, 6-4 win over Martin Klizan of Slovakia while Federer made it into the third round by downing Julien Benneteau of France 6-2, 6-2.
Federer is trying to win for the second time at Wimbledon in as many months. He captured a grand slam title at the historic stadium this summer and is now seeking a gold medal in the Olympic tournament being played on the same courts.
Roddick's victory set up a second-round match against No. 2 seed Novak Djokovic. Federer's third-round opponent will be Denis Istomin of Uzbekistan, who defeated Gilles Muller of Luxenbourg 6-7 (4-7), 7-6 (7-3), 7-5.
No. 11 seed Nicolas Almagro of Spain coasted in his second-round match against Russian Alex Bogomolov 6-2, 6-2 while first-round winners Monday included Juan Monaco of Argentina, Marin Cilic of Croatia, Richard Gasquet of France, Marcos Baghdatis of Cyprus, Lleyton Hewitt of Australia and Milos Raonic of Canada.
In the women's draw, Azarenka won her postponed match with Irina-Camelia Begu of Romania 6-1, 3-6, 6-1.
Americans Venus and Serena Williams advanced as well -- Venus breezing by Italy's Sara Errani 6-3, 6-1 in a first-round duel and Serena getting to the third round with a 6-2, 6-3 decision over Urszula Radwanska of Poland.
Like Federer, Serena Williams is trying to back up her Wimbledon crown with an Olympic gold medal.
Petra Kvitova of the Czech Republic, last year's Wimbledon winner and seeded sixth at the Olympics, ousted China's Peng Shuai 7-5, 2-6, 6-1.