It is where he flexed his early muscles, where he whooped in delight after an extraordinary match with Richard Gasquet, where he has bashed the ball relentlessly under a roof as rain battered down, where he wept in dispiriting defeat, where he struck Olympic gold and where he celebrated the greatest moment in his career with a clenched fist and a climb into the players' box.
Yesterday the most famous court in the world became the venue for his coming home party at SW19. Murray, the defending champion, also made it his playground.
The boyish David Goffin, displaying the early nerves of a pupil on his first day at the big school, was dismissed in two hours, two minutes, 6-1, 6-4, 7-5 by the buoyant Murray. It was not quite a bullying, but it came close.
Goffin, the world No.104, forced only two break points - both saved - on an imperious Murray serve and the 27-year-old Scot powered his way to victory with that mixture of belligerent power and deft touch that has marked him as a champion.
The Murray serve statistics brook no argument. He achieved a 71% rate on his first serve, winning 85% of points on it. He hit eight aces, finishing the match with one, at speeds of up to 131mph.
Goffin, who has never beaten one of the big boys, losing his nine previous battles with top-10 players, entered the arena with all the confidence of a schoolboy whose dog has just devoured his homework. Murray, in contrast, strolled in with the air of the superhero who had just saved a labradoodle from death on a road on his way to practise at Wimbledon on Sunday.
This as all the hallmarks of a spoof story but, almost incredibly, it happened. The runaway dog was returned to its owners and SuperAndy subsequently donned his white togs and loped through to the second round yesterday.
Murray was greeted by an extraordinary roar as he walked on to court and said his nerves were dispelled by a quick start against Goffin. The problem for the Belgian was that he was no problem to Murray. Goffin is a gifted player but does not have the weapons to unnerve the world No.5.
Murray thus could hold serve with regular ease and then put pressure on his opponent's game. Goffin occasionally thrilled the crowd with passing shots but this was Murray's day.
The Scot broke Goffin in his first attempt and romped to the first set in 29 minutes. The match became progressively more awkward for Murray, but no more than that.
He later described the match as being of high quality in the second and third sets. It was, but that is not to confuse technical excellence with any doubt about the eventual outcome.
One break of serve in each of the second and third sets were enough to despatch Goffin, whose best Wimbledon performance is to reach the third round and whose priority seemed to be to make the score respectable.
Murray, of course, has the highest ambition at Wimbledon. He has reached the semi-final, at least, since 2009 and his report card for his performance yesterday would be studded with As.
His serve was excellent, his return game predictably accomplished and he was strong off the forehand and adept on the backhand, deploying that devilish slice that creates problems for his opponents and opportunities for him. His highlight package must include a wonderful lob in the first set that left Goffin as bemused as a first-year pupil confronted by the horrors of calculus.
Murray, in short, was a very good boy somewhat removed from his past as a mischief-maker.
The Scot, guest editor of the most recent Beano, admitted to the press: "I was a bit like Dennis probably. I wasn't particularly well-behaved when I was a kid. My mum would definitely say that."
Having revealed Dennis the Menace as his alter ego, Murray decided he would no longer play along with recurrent questions about England and the World Cup.
"I'm here to do my thing. I don't think that the English football team get asked about me in their press conferences," he said. "So I'd appreciate it if that wasn't brought up when I was playing because I'm yet to hear Wayne Rooney talk about my matches at Wimbledon. I don't think it's fair."
This was said quietly but firmly. The message was relayed in a manner that brooked no misunderstanding. It was an example of the sort of communication that Murray values from Amelie Mauresmo, who will coach him through the summer at least.
"There could be 100 coaches that might be trying to get me to do the same thing, they might be getting me to come to the net more.
"Everyone could say the same thing, but it's about how you say it, how you get through to the pupil basically," he said.
Murray looked far from a pupil yesterday. He was composed and in command, both on-court and off-court. He moved through to the second round as normal. The scenes on Centre Court have changed over the years for the 27-year-old Scot but one trait has been constant: Murray never loses in the first round at Wimbledon.
This, too, was his 450th victory in Tour-level matches. He now faces a second-round match against a player who is simply not in his class. But if Goffin was a schoolboy in comparison to Master Murray, Blaz Rola, his next opponent, is just out of the nursery, with only a year on tour behind him.
The Slovenian defeated Pablo Andujar of Spain in straight sets, declaring with endearing, if fulsome honesty that he hoped he did not "poop his pants" when seeing the Scot on the other side of the net.
He also added: "I didn't see Andy's match but I don't think I needed to - I know what to expect. I don't think an up-and-coming tennis player could have asked for a better match-up, I'm facing probably the greatest sportsman in England in one of the greatest venues."
Murray was top of the form yesterday. Rola, though, needs to do more work on his geography.