Tiger Woods, a legend of the green whose body has begun to give way, relishes playing in his 26th Masters, beginning with Thursday’s opening round at Georgia’s Augusta National Golf Club.

At age 48, after multiple surgeries to his knees, back, leg, and ankle, Mr. Woods said this week his body “still hurts,” but he is hoping to win his sixth green jacket and tie the immortal Jack Nicklaus for the most wins in Masters history. “If everything comes together, I think I can get one more,” Mr. Woods said during a press conference on Tuesday.

The 15-time major champion last won the Masters in 2019, in a celebrated comeback from back fusion surgery. Since winning his first major here in 1997, he also collected green jackets in 2001, 2002, and 2005. He’s a longshot to win here this week, though. Last year, plantar fasciitis forced him to withdraw from the tournament after two rounds. 

The world’s top-ranked player, Scottie Scheffler, is the favorite to win his second green jacket this year. Jon Rahm is the defending champion and Rory McIlroy is seeking the elusive career grand slam. Yet if Mr. Woods is to win another major, it could come at Augusta.

“This tournament has meant so much to me in my life and my family. I think I’ve been playing here for, what 29 years now,” Mr. Woods said, including his appearances as an amateur. “It’s been part of my life to have won here as my first major as a pro. Hugging my dad, then a full circle in 2019 to hug my son. It has meant a lot to my family. It’s meant a lot to me. I always want to keep playing in this.”

Masters week is special in the golf world. It’s the only major on the same golf course each year, and invitations are prestigious. Included are reigning PGA Tour winners, recent major champions, leaders in the world golf rankings, and the select few the tournament committee decides to invite. It’s as close to a fraternity as professional golf gets. 

Mr. Woods reflects that those fortunate few “get to tell stories and catch up with friends and for me to get a chance to catch up with idols and people that I looked up to my entire life.” 

An automobile accident in 2021 caused severe damage to Mr. Woods’s right leg and for the last three years he has displayed a noticeable limp that has limited his ability to compete. Rehab and recent ankle fusion surgery have eliminated much of the limp, but, he said, “Some days I just feel really good and other days, not so much.”

While Mr. Woods believes he can contend here this week, at the very least he could set a record for 24 straight cuts made at the Masters, which is a significant accomplishment in itself. He currently shares the record for most consecutive cuts made at Augusta with Fred Couples, who is in the field, and Gary Player.

 “I think it’s consistency, it’s longevity, and it’s an understanding of how to play this golf course,” Mr. Woods said. “You still have to go out and execute, but there’s a lot of knowledge that goes into understanding how to play it. Every tee box has changed since the first time I played. Every green has been changed. But the overall configuration of how they roll and how they move and the angles you take that hasn’t changed.”

Mr. Woods was 5 years old when he played in his first golf tournament. Fame, hardware, and financial riches have followed. “It’s allowed me to see places where that I don’t think I would ever have gotten a chance to see, the people that I’ve got a chance to meet all around the world,” he said.

Mr. Woods is active in the political and business dimensions of the sport. He was named the sixth player-director on the PGA Tour’s policy board, which was formed in response to a potential merger between the PGA Tour and LIV Golf. Mr. Woods has participated in negotiations with the PGA Tour commissioner, Jay Monahan, the DP World Tour, and Saudi Arabia’s Public Investment Fund, which funds LIV Golf. 

In March, Mr. Woods also became part of the 13-member board of directors of the newly formed PGA Tour Enterprises, created out of the PGA Tour partnership with Strategic Sports Group. Enterprises  made an initial investment of a billion and a half dollars in the Tour and allows players to receive equity.

Mr. Woods could be the captain of the America’s Ryder Cup team when it challenges the Europeans at Bethpage in 2025. He says that he will meet with officials of PGA of America to have more formal discussions about leading the American team. Mr. Woods was the captain of the winning U.S. team at the 2019 Presidents Cup in Australia. 

“Let me focus on getting through this week,” he said, “and hopefully getting another jacket. Then we can sit back and talk about it next week.”