|ATP World Tour Finals|
|Venue: O2, London Dates: 15-22 Nov Sessions: 14:00 and 20:00 GMT|
|BBC coverage: Watch live on BBC TV, listen on Radio 5 live sports extra and follow live text updates on the BBC Sport website. Full details.|
Novak Djokovic began his bid for a record fourth straight end-of-season title with victory over Japan's Kei Nishikori at the ATP World Tour Finals.
The Serb won 6-1 6-1 in 65 minutes to seal his 15th consecutive win at the O2 Arena, a run stretching back to 2011.
Roger Federer beat Tomas Berdych 6-4 6-2 in 69 minutes, in the opening day's other round-robin match in London.
Britain's Jamie Murray won on his debut as he and doubles partner John Peers beat Simone Bolelli and Fabio Fognini.
All the players wore black ribbons on their shirts as a mark of respect to the victims of Friday's deadly attacks in Paris.
"All my heart goes out to the families of the lost ones, it's really devastating to see those images and that footage," said Djokovic.
Djokovic dominance continues
The world number one needed just over an hour to see off eighth seed Nishikori, and ended the afternoon with a trophy in his hands as he was confirmed as the 2015 world number one.
Djokovic, 28, won the Australian Open, Wimbledon and US Open, and went within one match of the calendar Grand Slam, losing to Stan Wawrinka in the French Open final.
"Undoubtedly it has been the best season and the best year of my life - I became a father and I got married. Those are the kind of trophies and milestones that mean the most to me," he said.
|Stat of the day|
|Djokovic won 57% of points on Nishikori's first serve and 56% of points on Nishikori's second serve.|
"I've been experiencing the peak time right now of my abilities. I was very consistent with my results, 2011 and 2015 definitely stand out.
"My team plays a big part in this - I have a great team of experts and most of all they are my friends and people I can rely on."
Nishikori, 25, did not serve well enough to give Djokovic any trouble and was broken five times as the Serb extended his latest winning streak to 23 matches.
|BBC Sport analyst Tim Henman|
|"That was normal service resumed for Novak Djokovic, a real clinic out there. He only lost nine points on serve, hit the ball very cleanly and dominated in all aspects."|
Federer finds his range
Djokovic might be the dominant force right now but Federer holds a record six end-of-season titles and remains the fans' favourite.
A large number of travelling Swiss swelled the capacity evening crowd as their man found his form to rack up his 49th win in 60 matches and 14 trips to the season finale.
Federer started surprisingly poorly, double-faulting twice as he dropped serve to love in game three, only for Berdych to return the favour in the next game, almost tripping over when a drop shot caught him out.
The Czech, 30, was struggling to find any rhythm and eventually paid for a first-serve percentage of just 41% as three errors handed over the key break at 4-4.
Federer took complete control with seven games in a row for a 4-0 lead in the second set and promptly wrapped up victory.
The Swiss will take on world number one Djokovic in the second round of Stan Smith Group matches on Tuesday.
"It was one of the worst starts I've had in years," said Federer. "No first serves, two double-faults, nothing coming from the baseline. So it was rough.
"But thankfully I was able to pick it up. I mean, the surface does play slow here. If you get to see too many second serves, clearly you can crawl back into the match. You can get your chances from the baseline to find rhythm quickly."
Murray wins on doubles debut
Jamie Murray and Australian Peers won a dramatic opening match against Italians Bolelli and Fognini 7-6 (7-5) 3-6 11-9.
That gives them an early lead in the round-robin stage, with Bob and Mike Bryan to face Rohan Bopanna and Florian Mergea later on Sunday.
Murray and Peers are seeded fourth for the tournament and could end the year as the world number one pairing, but have already agreed to go their separate ways in 2016.
"I didn't really think about it that much," said the 29-year-old Scot, who will play with Brazil's Bruno Soares next year.
|When's Andy playing?|
|Jamie's younger brother, Andy, plays his opening singles match against Spain's David Ferrer at 14:00 GMT on Monday, a match you can follow live on BBC Two, Radio 5 live sports extra and the BBC Sport website.|
"From my point of view, we just try to do the best we can, finish on a high and try to make a great year even better."
Murray also has Great Britain's Davis Cup final against Belgium to look forward to later this month.
"It's an exciting time for me," he said. "It's lots to look forward to, obviously starting with today.
"It's a huge event for us which we're really excited to be a part of. We worked hard all year to qualify for this tournament.
"We want to make the most of our time here. When that's done, then I'll think about Davis Cup."