WIMBLEDON, England — All tennis players have goals, perhaps a top 20 ranking or a few victories in a Grand Slam event. Then there are dreams: the no. 1 ranking, major titles, fame, fortune. Aravane Rezai, a 20-year-old who won her first ever match at Wimbledon yesterday, prefers outlandish fantasies.

“For me, no. 1 is actually too simple,” Rezai said. “My goal, my dream is I want to win the Grand Slam, you know consecutive, four Grand Slams, for five years.”

Yes, you’ve read that correctly: 20 major titles in five years, a stretch of dominance that would surpass anything ever seen in men’s or women’s tennis. It’s a bold wish for a woman who has won eight matches this year against 15 losses and has never won a title on the WTA Tour. Her 6–2, 7–6(4) victory over Shenay Perry, on Court 19, was her first at a Grand Slam tournament since last year’s U.S. Open, where she reached the fourth round — the best result of her career. At the Australian and French opens earlier this year, Rezai lost in the first round. She also lost eight matches in a row from January until April.

These facts and figures do not concern Rezai in the slightest, and that’s no wonder considering how improbable it is that she’s playing professional tennis at all.

Rezai picked up a racket at age 7, after a few years of watching her older brother, Anauch, who now travels and hits with her. She didn’t take lessons from professional coaches and didn’t schedule blocks of time at fancy tennis clubs. Her father, Arsalan, and mother, Nouchine, grew up in Iran before immigrating to France. They had no money and knew nothing about tennis. Yet Arsalan taught his daughter the game, often in outdoor winter practice sessions. When Aravane won a tournament for girls two years older than her, he pushed her to practice harder. In recent years, as they went from tournament to tournament to boost Aravane’s ranking, the Rezai family traveled in a van, and slept in it, to save money. At one tournament in February 2006, in Ortisei, Italy, Aravane said the temperature dropped to about minus 4 degrees. She qualified for the tournament and defeated two players in the main draw, including the no. 19-ranked woman in the world.

“When I go on the court I say, ‘Okay, I have to win,'” Rezai said. “I cannot lose against her, she sleep in the hotel. She [has] more money than me and she’s not practicing more than me. Why [do] I have to lose?”

When asked to name her strength as a player, Rezai responded, “mental.” She said she owed her confidence to her father, who studied geology and worked as a car mechanic before quitting his job to train his daughter fulltime. In her early days, however, Rezai wasn’t so thrilled by his grand plan for her future.

“When I started, he pushed me,” she said. “I can’t choose my destiny, he have to choose and he chose like that. And now I’m actually very happy for that. I think every girl they want to have my place. After years, I learned to like tennis and when I won many tournaments, you feel happy. It was very hard for him to believe one child, 7 years old, to believe in this girl.”

Rezai is undersized at 5-foot-5-inches, still has no clothing sponsor, and is hardly in optimal physical condition. She’s reached as high as no. 40 in the world because she strikes the ball as powerfully as any woman on the tour, especially with her two-handed backhand. Rezai’s strokes are short and explosive, and often produce winners in unlikely situations.

Arsalan remains Rezai’s coach, but he and his daughter recently enlisted Patrick Mouratoglou, whose academy trained Marcos Baghdatis, for part-time help. Mouratoglou sees great potential in Rezai, though he believes it’s unrealistic to expect immediate results from her. Rezai needs to work more on her fitness, lose weight, improve her serve, and develop more consistency. This year, he wants her to maintain her ranking so she can begin to build on it next season.

“She reached the top 50 in the world with a lot of areas that she can improve not 100%, but close,” Mouratoglou said. “She has to do what needs to be done in the next three years. If she doesn’t do so, then she’ll be in trouble, so it’s now.”

At Wimbledon, Rezai has a chance to win another match. In the second round, she’ll face Francesca Schiavone, a fit, consistent Italian who rarely succeeds on grass: She’s reached the third round of Wimbledon one time in six tries. After Schiavone would come Ana Ivanovic, the 19-year-old French Open finalist who in the next few years might have a thing or two to say about Rezai’s Grand Slam fantasy. Not that Rezai is about to give up the chase.

“It’s maybe hard to do it, but if I work every day, if I’m serious, then why not?” Rezai said. “Why Federer? Why Borg? Steffi Graf? Why not me?”

She has modest plans for her life after tennis, too: Astrophysics.

“If I have a good result here I want to build a big telescope to watch the stars,” she said. “Life is not only tennis.”

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Rain interrupted play yesterday before Roger Federer could finish off Juan Martin del Potro, and before Tim Henman could finish three games against Feliciano Lopez. Andy Roddick, Serena Williams, Justine Henin, and Jelena Jankovic had better luck. All four advanced to the third round.

tperrotta@nysun.com