The advertisements for the $250,000 Colgate Series Championships, which begin Wednesday at Capital Centre, ask the tantalizing question: "Who will win the battle for No. 1 in women's tennis?"

But they don't specify for which year.

The tournament is technically the grand finale of 1980, a curtain call for last season's stars one week into the new year.

The eight players involved -- Hana Mandlikova, Chris Evert Lloyd, Tracy Austin, Wendy Turnbull, Martina Navratilova, Andrea Jaeger, Virginia Ruzici and Pam Shriver -- qualified by finishing as the top point-winners in the 1980 Colgate Series of 39 tournaments around the world.

Twice in recent years, the top ranking has not been definitely settled until this final playoff. Thus, the "Who's No. 1?" come-on.

This time, however, most authorities agree that Evert merits summa cum laude honors for 1980, regardless of what happens here. The tournament is less provocative as the last roundup of 1980 than as the first skirmish of 1981, which promises to be a fascinating year for the suddenly wide-open, vibrant and prosperous women's game.

Evert compiled a 71-7 record in 1980, winning eight of the 15 tournaments she played, including the U.S., French, Italian, Canadian, and U.S. Clay Court tourneys. She was runnerup at Wimbledon to Evonne Goolagong Cawley.

Returning to competition in May following a four-month sabbatical, she lost only three matches the rest of the year -- to Goolagong, Mandlikova and Navratilova. She beat Austin -- the nemesis who had drubbed her three times in 10 days last January -- in the semifinals of the U.S. Open, and completed the climb back from No. 3 to No. 1 in the computer rankings of the Women's Tennis Association.

Austin, 18, was Evert's only real rival for the No. 1 ranking. She won 88 of 96 singles matches, 11 of 21 tournaments. She had a 3-1 record over Evert and won the Avon Championships, the climactic playoff of the winter tour, but was knocked out of Wimbledon and the U.S. Open in the semifinals. Her loss to Evert in the Open probably cost her the top ranking.

Austin thinks that if she wins the tournament here, she deserves consideration shared by Shriver and some others.

But Evert considers herself secure at the top of the 1980 totem pole, and most experts concur.

The two leading American tennis magazines have declared her No. 1. The panel of former-champions (Althea Gibson, Ann Jones, Margaret Osborne duPont) that selects the International Tennis Federation's world champion is believed to be leaning heavily in the same direction. The chief dissenting opinion belongs to the U.S. Tennis Association, which recently issued its 1980 American rankings, with Austin No. 1 and Evert No. 2.

"I think Chris has it clinched," said Navratilova, the undisputed world champion of 1979 who won her first five tournaments and 28 matches in 1980, then slumped to an 86-13 record for the year, losing in the final of the Avon Championships, the semi-finals of Wimbledon and the quarter-finals of the U.S. Open. "She didn't play the Avon, but she had the best record in the other major championships. She's also No. 1 on the WTA computer, which to me is the deciding factor." s

That does not diminish the appeal or importance of the upcoming tournament, an all-star overture for a year bursting with promise.

Last year saw a significant changing of the guard in women's tennis. Dependable old favorites such as Virginia Wade, Betty Stove and Rosemary Casals, who were in the top 10 through most of the '70s, declined. Goolagong, after her sentimental triumph at Wimbledon, has retired temporarily -- and perhaps permanently -- to have her second child. Kerry Reid also took maternity leave, and may not return. Billie Jean King, who climbed back into the top five by midsummer before illness cut short her season, underwent her fourth knee operation in the autumn, and could find it difficult to make another successful comeback at age 37.

Evert is back on top, to the astonishment of those who had counted her out, but Austin and Navratilova remain at her heels. Meanwhile, teenagers Mandlikova, Jaeger and Shriver have vaulted ahead of the old middle class -- the Dianne Fromholtzes and Greer Stevenses of the world -- and joined the power elite.

Mandlikova, 18, had an outstanding last quarter of 1980, winning six tournaments from the middle of August to the end of the year, and reaching the final of the U.S. Open. She is a gifted athlete and shotmaker, exciting to watch, a net-rusher always capable of soaring to dizzying heights or crashing just as spectacularly.

Jaeger, 15, is a delightfully spunky scrambler whose long, blond braids fly through the air as she chases down shots all over the court. Another fine athlete with an instinctive flair for the game, she is the youngest player to crack the top 10 in the modern era. She made her pro debut on the "Futures" circuit less than a year ago, but swiftly graduated to the major tour, reached the quarterfinals at Wimbledon and the semifinals of the U.S. Open and wound up the year with a 60-19 record and $220,496 in prize money.

Shriver, who reached the final of the U.S. Open as a 16-year-old in 1978, got back on track last year following a disastrous 1979 in which she struggled with a shoulder injury as her computer ranking plummeted from No. 12 to 47. She climbed steadily through 1980, losing only once to a player ranked below her from February on, and arrived in the top 10 after beating Navratilova in Australia in November.

The average age of the qualifiers for this year's Colgate Series Championship is 21 1/2 years. Turnbull and Evert are the old ladies at 28 and 26, respectively. Last year, the average was nearly 25.

"Shoot, we've been coming on pretty strong, all of us, so it's nothing too new at this point, having the teenagers doing well," Shriver said. But then she thought about it for a minute, and realized this could be a landmark year, the season the kids storm the citadel.

"I think Martina and Chris are going to remain in the top five at least for another couple of years, and obviously Tracy will be up there," she said. "I think Evonne will slip out, Mandlikova will move up at least to No. 4 and Jaeger will be No. 5 pretty soon. So you'll have three of the top five under 20 years old. I don't think that's ever been, has it? I think it's great for women's tennis, all this new blood coming towards the top, because maybe people were getting a little sick of the same players all the time."

Austin thinks the eight women here will be difficult to dislodge in 1981. "The depth is amazing right now. I think just about anybody in the tournament could win. Even the first round here is tough," she said, pointing to Wednesday's opening day pairings: Navratilova-Turnbull and Austin-Ruzici in the afternoon session, starting at 1, followed by Mandlikova-Jaeger and Evert-Shriver at night, starting at 7.

Austin is being kind when she says anybody could win this tournament. Navratilova and Evert are more realistic when they suggest that four players have a reasonable shot: themselves, Austin and Mandlikova.

"Any of the other four could beat anybody or even get to the finals, but I don't think they could win it," said Navratilova. "They've all been spoilers in the past. They have a chance in every match. But I don't think they could put together the four-day perfection it would take to win the whole thing."

The women do not have a rivalry like Bjorn Borg versus John McEnroe, which has captured the imagination of the general public, but the appealing newcomers have stirred new interest among tennis fans. The prospects are bright.

"I think 1981 will solidify the new sprouts in women's tennis and see the phasing out of the old guard: the Goolagongs, the Wades, the Kings," said Jerry Diamond, executive director of the Women's Tennis Association. "They will be the Arnold Palmers of our tour -- when they appear they'll be popular, but nobody will expect them to do that much.

"I think if we can come up with one new face in 1981, one kid who can make the progress that Mandlikova and Jaeger did, we'll keep pace. I think that's pretty much what you need, one bright new kid every year."

Certainly the incentive, and the opportunities, are there.

Women's tennis has an outstanding "minor league" -- a growing network of "Futures" and satellite tournaments with open entry. Any aspiring player can plunk down the entry fee fee and get into the qualifying tournaments. If they are good enough, they can move up rapidly.

The top women are making more than a comfortable living. Of the eight singles players in the Colgate Series Championship, prize-money earnings ranged from Shriver's low of $171,104 to Navratilova's high of $797,487.

Austin collected $642,378, not including endorsements, and she's still in high school. Even Ruzici, hardly a household name, made $190,936. Turnbull won only two tournaments in singles, but with her doubles income totaled $308,413. Evert won $448,533 in her limited season, and recently signed the largest endorsement contract ever commanded by a woman athlete: $7 million over five years from Ellesse, the Italian sportswear manufacturer.

Eighteen women surpassed $100,000 in prize-money earnings in 1980, and 35 players topped $50,000. The total purses for the women's tour will rise from $9.25 million in 1980 to $10.5 million in 1981, with the bulk of the increase fattening the wallets of the players ranked between No. 20 and No. 70.

The women have been less greedy than their male counterparts, more conscious of the need for controlled growth as the foundation of a healthy future.

For most of the year, there is only one major women's tournament in a given week. If the top women are playing, they are in it -- not competing in an exhibition or "special event" somewhere else. The WTA for years has guaranteed tournaments a certain number of top players, based on the prize money they put up.

Women's tennis is, on balance, looking rosy. The tour has not lost a tournament or sponsor in three years. It is attractively packaged and smartly marketed, with relatively little of the gluttonous infighting that fragments men's tennis. An ill-advised proposal that the women secede from the U.S. Open and set up their own national championship was wisely turned down last fall.

The scene is alive with fresh faces and more depth than ever before, an enticing mixture of young and old, conservative and bold.

The main unsettled question is who will win the battle for No. 1? In 1981.