That's the end of the first day of the ATP World Tour Finals. There'll be more on Monday, featuring Andy Murray and David Ferrer at about 14:00 GMT, and Stan Wawrinka and Rafael Nadal at about 20:00 GMT.

Thanks for joining us. We'll see you a little before 14:00 GMT tomorrow as Murray starts his campaign. 

Federer will now have time to prepare for his next match, a potential humdinger against Novak Djokovic on Tuesday. Both were clinical in their opening matches. Djokovic, of course, will be favourite.

He's a man who is aiming to win a record fourth successive title, a man who lost only seven points on his serve in beating Kei Nishikori earlier 6-1 6-1. 

Federer is still on court signing autographs, and there are quite a few people wanting the Swiss' signature on their super-sized tennis balls. Smartphones are capturing the moment, too. The Swiss signing everything in his sight, and posing for photographs. He might be there a while at this rate. 

Image source, Reuters

Roger Federer on receiving the fans' favourite and sportsmanship awards: "It's very special. I enjoy getting awards, especially ones by fans and fellow players. I try to do it with style, I play hard but it is nice to get this respect. I try to behave well to my opponents and the tournaments, but I used to be tough on myself.

Russell Fuller
BBC tennis correspondent

Federer steps back on court to receive two prizes, one being the fans' favourite award and other the Stefan Edberg sportsmanship award. They're two beautiful deep glass vases, just the job for a bowl of punch during a Christmas party.

Piers Newbery
BBC Sport at the O2 Arena in London

It might be just what Federer was after, and fun for his multitude of fans, but another one-sided match to follow Djokovic's earlier demolition of Nishikori is not great for the tournament. 

Last year's group stage did not see a three-set match until the final round, and only one set went to a tie-break. It is a mark of how big a gap there remains between the good and the great, but we could do with a bit more competition in the early stages this year.

Jamie Delgado
Former Great Britain Davis Cup player on Radio 5 live sports extra

Image source, Getty Images

A thunderous forehand into the corner from Berdych secures the Czech a hold to love, but he's just delaying the inevitable. Just a matter of time before he's shaking hands with Federer at the net. 

Jamie Delgado
Former Great Britain Davis Cup player on Radio 5 live sports extra

Berdych makes the most of a weak Federer second serve to battle to 30-30, but the Swiss responds with a clinical ace down the 'T' for a 40-30 lead. If there was hope for Berdych, there certainly isn't now as the world number three delicately places a backhand out of his reach. The Swiss one game from victory. 

Image source, Getty Images

Berdych isn't amused but the spectators are very much entertained as Federer produces another delicate backhand dropper to open the game. 

That shot seems to have stirred something in Berdych as he rattles off two beefy serves to nudge 30-15 ahead. But the Czech can't seem to shake Federer off his tail. 

But at 30-30, Berdych comes up with another booming serve and the 30-year-old keeps the points short to succeed where previously he has failed. 

An admiring intake of breath from the crowd as they watch a dreamy backhanded dropper from Federer. There's no neutrality inside the arena. Swiss flags are being waved. Decibels rising as the Swiss proceeds to 40-0. Berdych fails to keep the next return on target. Federer cruising. 

Jamie Delgado
Former Great Britain Davis Cup player on Radio 5 live sports extra

Image source, Rex Features

Federer keeping the ball low, which is a canny ploy against the giant Czech. Berdych drags himself back into contention at 30-30, but he has the body language of a man who is climbing Everest in flip-flops. He knows it's not end well, but he's going to halfheartedly give it a g anyway. 

To deuce we go. Berdych long, long, long. Break point Federer. 

A nervy baseline slug-fest ensues... from tramline o tramline they go.. who will falter? Berdych goes for broke, and misjudges the forehand... 

Federer, break in the bag, is untroubled on his serve. It's only at 40-0 that Berdych ignites some sort of a rally, but it ends as quickly as it started with a Berdych forehand into the tape and it could soon be goodnight Vienna. 

Berdych hasn't won his opening round-robin match in five of his previous season-ending tournaments, and he needs a dramatic change in fortunes if he is to come away with a win tonight. 

The crowd with a first chance to holler and whistle in admiration at a series of eye-catching shots... Berdych, backpedaling, scooping a shot over his shoulder... Federer at the net, waiting to pounce with a volley. The crowd enjoyed it. 

From 30-30 to break point Federer. The Swiss returning the Berdych serve with ease, and the Czech sleepily directs a forehand into the tape to gift the former champ the game. 

Piers Newbery
BBC Sport at the O2 Arena in London

Image source, Getty Images

It's hard to look menacing in beige, and Berdych showed a familiar frailty at the decisive moment with a flurry of errors to hand over the set. A man in front of me stands up to reveal the word 'ROGER' emblazoned across the back of his red shirt. I've yet to see a 'TOMAS'.

Image source, Getty Images

Federer hasn't been at his best in this match, yet he finds himself serving out the set. The Swiss serving with the accuracy of his country's clocks, advancing to 40-0 with little fuss. 

Berdych with plenty of time to place a thumping forehand beyond Federer, but he needs to produce those sort of shots on a more consistent basis. The Czech, on the next point, with oodles of time, rashly swings at a forehand which bounces long and that's that.