Ivan F. Boesky really plays the stock market. Like a fine violin, maybe, or the way Brooks Robinson used to play third base. A master.

Resembling a surfer catching a wave, he tries to grab onto stocks being driven up by corporate machinations such as mergers or proxy battles and ride them to the top. It demands precise timing, shrewd sense, and, ideally, a pile of money to bet (or lose)--and Boesky, 46, is worth something in the neighborhood of $100 million, by one estimate.

The game he plays is called risk arbitrage, and it's one that's moved from Wall Street's back rooms to America's front pages in recent years as the actions of arbitragers such as Boesky have played key roles in such notorious merger battles as those for Conoco Inc., Cities Service Co. and Martin Marietta Corp.

Even in less spectacular transactions, the "arbs" usually can find an angle. Boesky, through his Ivan F. Boesky Corp., currently is playing the takeover of Lifemark Corp. by American Medical International Inc., buying Lifemark stock at about $36 a share and, if the deal goes through as planned, hoping to exchange it for AMI stock worth about $46 a share--a tidy profit.

And, like the rest of Wall Street, Boesky currently is keeping a close eye on the skirmishing between Mesa Petroleum Co. and Gulf Oil Corp., in the hope that Mesa Chairman Boone Pickens' raid on Gulf will force developments--such as an offer by another company--that will send Gulf stock skyrocketing. Just in case, Boesky already has begun buying Gulf stock. "Obviously, it catches one's attention," he says dryly.

Boesky certainly did not invent arbitrage, but he claims a good deal of the credit for making it a big-time Wall Street activity. He even teaches courses in the subject at the business schools at Columbia and New York universities.

Before Boesky and a handful of other pioneers came along, arbitrage was pretty much the private game of a few Wall Street titans. What Boesky did was to make arbitrage a mainstream business for big brokerage firms, something that was accomplished principally by getting institutional investors interested in the game. He started his own arbitrage house--another first--in 1975, and his second, his present company, in 1980.

Arbitragers are perhaps at their best in an acrimonious takeover battle, when competing offers start flying and traders have to scurry to buy stock at the lowest possible price and then sell it to one of the takeover competitors for the best possible price.

The trick is to get in as early as possible--a $2 or $3 difference in stock price can mean millions of dollars--and as a result, firms doing arbitrage work employ sophisticated intelligence-gathering systems to take the pulse of developments in a takeover war and have facilities for fast trading to take advantage of events.

But arbitrage is not without considerable risk. Just ask Boesky about Cities Service. "C-c-c-c-cities S-s-s-s-service?" he stutters, then laughs. "As in all things, not everything materializes."

Last year's battle for Cities Service was very nearly the Little Big Horn of the arbitrage business. Just when the arbs thought they'd made a killing on Gulf's $63-a-share offer for Cities--about twice what the professionals had paid for the stock--Gulf got cold feet and backed out of the deal. After three weeks of nail-biting and plummeting stock prices, Occidental Petroleum stepped in and bought Cities' shares for about $52 a piece, saving the arbs from ruin.

Still, Boesky argues, arbitrage isn't as risky as it's been protrayed to be. "Once you leave the bank and take your money out from under the mattress, you begin to expose yourself to risk," he says. "But risk is a relative matter." Claiming that his arbitrage investments have outperformed the Standard & Poors' 500-stock index by a factor of 10 in the past few years, Boesky says that arbitragers have better control over their fate than more traditional investors who can be hurt by the vagaries of the stock market.

"I believe one day . . . that arbitrage will be perceived as a conservative investment," he says. "But from the outside looking in, they say, 'Nonsense, that's riverboat gambling.' "

Like any good market player, though, Boesky is hedging his bets--although he prefers to describe it as diversification. Arbitrage, at best, is a cyclical business--a good takeover bid sometimes is hard to find--so Boesky's firm is moving into investment banking, or, as he calls it, "venture arbitrage."

In other words, the firm is investing in companies even when they aren't involved in some sort of corporate power play. The standards are the same: Boesky looks for companies that appear to be undervalued with a good chance for stock appreciation in the near future. One reported recent investment: RCA Corp., although Boesky will not comment on that. The company also is involved in the leveraged-buyout field, in which investment bankers put together corporations--usually involving spin-offs of divisions of larger companies--whose financing is secured by the business' assets.

Boesky says that his company's diversification makes it "a deal emporium," with a portfolio of investments in corporate situations that will reach fruition at various times--quickly in the case of traditional arbitrage situations, more slowly for investments in undervalued companies. "These two cycles, co-existing in the same portfolio, are really complementary to each other," Boesky says.

"We're sort of a throwback to an earlier era," he says of his company's strategy. "This is what Wall Street kind of was--it was a place where people risked capital for appreciation."