(FORTUNE Magazine) – YOUNG, RICH, POWERFUL, AND CHANGING THE WORLD Work your way up from the bottom? Forget it. Our list of 40 (okay, 41) who have vaulted to the top before they hit 40.

The 40 under 40 captures the American dream--rising from nothing and nowhere to achieve wealth and power--and combines it with the American obsession: speed. In the pages that follow, you'll see whiz kids who have managed to get to the top, to change the way businesses and consumers think, and to make boatloads of money before many have even started rinsing with Grecian Formula.

For a time in the late 1990s and early 2000s, achieving this kind of quick success looked remarkably easy: (1) start a dot-com; (2) retire. And for the past five years FORTUNE has chronicled those who did it well, compiling a list of the 40 richest Americans under 40. But now, with so many tycoonlets "consulting" or back with the companies they had planned to bury, measuring success has become much more nuanced.

So this year we broke our list into four: We'd keep measuring wealth, sure, but also look at those who wield the most influence, who show the top entrepreneurial promise, and who have the most beautiful minds. The ground rules: No one could appear on more than one list (otherwise Michael Dell would pop up atop each), and only Americans or those working for American companies would be considered.

We calculated the "rich list" by combing through numbers from SEC proxies and stock-sale forms and by working with banking and real estate sources to divine valuations and property assessments. For the list of influentials, we scouted out leaders who control money, garner respect, and wield wide influence, from Linus Torvalds's Linux revolution to Aerin Lauder's transfiguration of global beauty. We ranked them based on interviews with peers and industry watchers--and after weeks of debate. Finding entrepreneurs was trickier; the proven ones made it to the rich list. So we found ten to watch--individuals who take chances, starting unusual and successful companies. Finally, the innovator list, which like entrepreneurs is unranked, falls furthest from the 40 Under 40's original goal. This group chases ideas, not money--though they don't turn that down--and have made their work transcend the theoretical world of the lab to apply to real life.

Ranking young success may have been easier during the boom, but it's a lot more fun now. --J.B.

THE TOP 10 MOST INFLUENTIAL In a short time this crew have become much followed (and in some cases feared) in their industries.

1 SALLIE KRAWCHECK, 38, CEO, Smith Barney Wall Street's "Ms. Clean" heads the $5.7 billion No. 2 research brokerage. The former CEO of Sanford Bernstein, Krawcheck delivered unbiased research when Wall Street was still delivering analysts to clients. Now the Street is watching to see if she can make research--and Citigroup--respectable again.

2 JEFF ZUCKER, 38, President, NBC Entertainment Programming prodigy Zucker helmed NBC's Today at 26, then led NBC to dominate prime time. Rivals still try to copy his format. He's in it for the long run: Zucker's a leading candidate to run all of NBC.

3 LINUS TORVALDS, 33, Fellow, Open Source Development Lab Torvalds dreamed up Linux--now he controls its growth. He has big allies and bigger enemies. IBM has adopted Linux; Microsoft abhors it.

4 B. KEVIN TURNER, 37, CEO, Sam's Club; Executive VP, Wal-Mart The former Wal-Mart cashier became its CIO at age 34 and revamped the firm's entire tracking and sales technology; peers raced to keep up. Now he's turning around the uber-retailer's 46 million-member Sam's Club.

5 LACHLAN MURDOCH, 32, Deputy COO, News Corp. Rupert's oldest son controls what Americans watch and read. As the No. 3 at News Corp., Murdoch oversees the U.S. publishing business and the company's 35 TV stations.

6 DON A. MATTRICK, 39, President, Worldwide Studios, Electronic Arts Another programming prodigy: At 17, Mattrick coded his first videogame, called Evolution, then built a company to market it. He sold to EA in 1991. Now he oversees all the giant's studios and programmers and has moved from virtual to real strategies.

8 STEVE JURVETSON, 36, Managing Director, Draper Fisher Jurvetson With hits like Hotmail and software company Interwoven, he has VCs watching what he's buying. Lately he has been looking at nanotechnology and molecular electronics to invest DFJ's $3 billion in capital.

8 BRYAN NESBITT, 35, Executive Director, GM Design While he was at DaimlerChrysler, Nesbitt's hip PT Cruiser steered in the cash, forcing automakers to ape his design thinking. One company went further: GM hired him to breathe life into Chevrolet.

9 AERIN LAUDER, 33, VP of Global Advertising, Estee Lauder Stylemaker, businesswoman, and socialite, Lauder is helping make over her grandmother Estee's once-staid company with edgy new images of beauty that influence global style.

10 THEO EPSTEIN, 29, General Manager, Boston Red Sox In his first season Epstein, the youngest GM in baseball history, confidently trades players, holds down payroll, and appeases baseball's crustiest fans.

THE 10 RICHEST Dot-commers still dominate this annual ranking. But those from the wide worlds of sports and Wall Street are making inroads.

1 MICHAEL DELL, 38 CEO and Founder, Dell $17.12 billion

The list's perennial No. 1, Dell wasn't shy about naming his company after himself. Now he ties it even closer, dropping "Computer" from the corporate name to reflect the push into servers, storage, and PC peripherals. No. 1 last year with $16.49 billion

2 PIERRE OMIDYAR, 36 Chairman and Founder, eBay $7.06 billion

eBay's largest shareholder splits his year between France and Nevada, but spends his time (and money) as a full-time philanthropist. A recent gift: $10 million to alma mater Tufts to create a school for public service. No. 2 last year with $3.82 billion

3 JEFFREY BEZOS, 39 CEO and Co-founder, Amazon.com $4.85 billion

He still can't turn a profit, but Bezos has turned plenty into believers. His stock was Nasdaq's best performer last year, and a surge in sales from free shipping this year has made Amazon soar. No. 4 last year with $1.66 billion

4 JEFF SKOLL, 38 Chairman, Skoll Foundation $3.85 billion

Skoll co-founded eBay with Omidyar. Now he's working like him, not with him: donating time and money. His foundation encourages social entrepreneurship. He has personally pitched in $165 million since 1998. No. 3 last year with $2.18 billion

5 DAVID FILO, 37 Chief Yahoo and Co-founder, Yahoo $1.45 billion

Press-shy Filo abandoned his electrical engineering Ph.D. attempt at Stanford to start Yahoo with No. 6 on our list, Yang. But just in case this whole "Internet" thing doesn't work out, Stanford says he's on a leave of absence. No. 7 last year with $551 million

6 JERRY YANG, 34 Chief Yahoo and Co-founder, Yahoo $1.28 billion

Still guiding Yahoo's strategy, Yang helped lead its recent acquisition of Overture, a coup in bolstering its business against competitors. With new CEO Terry Semel, he's branching Yahoo out into new areas. No. 8 last year with $514 million

7 SERGEY BRIN, 30 President (Technology) and Co-founder, Google $900 million

8 LARRY PAGE, 30 President (Products) and Co-founder, Google $900 million

These two came up with the idea for a better search engine while working on their Ph.D.s in computer science at Stanford. In the early days of Google they resisted selling ads. Good thing they reconsidered: Google has been profitable since 2000, and FORTUNE estimates Google's 2002 revenues at $700 million. Now other privately held tech firms are waiting for Brin and Page to pick a date to go public. They hope a Google IPO will revive the market for dot-coms. Not on last year's list

9 DAN SNYDER, 38 Owner, Washington Redskins $740 million

After making a fortune selling his marketing and advertising company, Snyder is paying big bucks to revamp the Redskins, aggressively recruiting free agents and sacrificing draft picks. No. 6 last year with $664 million

10 KEN GRIFFIN, 34 President, Citadel Investment Group $725 million

Notoriously secretive Ken Griffin, who manages a $9.5 billion hedge fund, got started while an undergrad at Harvard, where he ran two investment partnerships from his dorm. He married this summer--at Versailles. Not on last year's list

THE TOP 10 ENTREPRENEURS TO WATCH It's been brutal lately for startups, yet these few found rich niches, from gangstawear to software.

SEAN "P. DIDDY" COMBS, 33, CEO and Founder, Bad Boy Entertainment P. Diddy transformed himself from bad-boy rapper to multimedia mogul. His empire starts at music and puffs out from there: Clothing line Sean Jean brings in $300 million annually, his Justin's restaurants serve diners in New York City and Atlanta, and in the works are licensing deals for everything from furniture to vodka drinks.

BILL NGUYEN, 32, President and Founder, SEVEN Networks Mobile-phone makers would be lost (or late) without Nguyen. His industrywide software allows Sprint, Cingular, and others to give their phones e-mail, calendar, and document access. Investors always ring twice: He sold his last telecom venture for $850 million in 2000.

MARC BENIOFF, 39, CEO and Founder, Salesforce.com Looks as if nobody told Benioff the bubble burst. He built a company that sells sales-automation software by the sip. Running at $100 million a year, Salesforce.com is ripe for an IPO.

ELON MUSK, 32, CEO and CTO, SpaceX PayPal's co-founder sold it to eBay for $1.5 billion in 2002, then launched SpaceX. Its plan: a rocket that can put a payload into orbit for $6 million.

JAGDEEP SINGH, 36, CEO and Founder, Infinera Make that investors ring thrice. Singh's sold two of his last three telecom companies. Now he's shrinking telecom components, creating high-power iridium phosphide chips that are cheaper than standard silicon.

JOE LIEMANDT, 35, CEO, President and Founder, Trilogy Liemandt has thrived in the bust by selling his enterprise software on a pay-for-performance basis. The price is right, and public companies, which crave predictable income, have trouble competing.

MARTIN ROSCHEISEN, 34, CEO and Co-founder, Nanosolar After selling eGroups, FindLaw, and TradingDynamics, Roscheisen tried retirement, then started Nanosolar, which produces low-cost solar cells with the power to remake the alternative-energy market.

SCOTT BLUM, 39, CEO and Founder, Buy.com After taking his Buy.com public in 2000, he bought it back in 2001 and kept building. Now he's expanding, launching an iTunes Music competitor for the PC and a QVC knockoff for TV.

CHAD MIRKIN, 39, Co-founder, NanoInk and NanoSphere This Northwestern prof combined his entrepreneurial spirit with award-winning nanotech research to launch two companies that miniaturize circuits and detect biomolecules.

LIZ LANGE, 36, President and Founder, Liz Lange Maternity The hottest player in the $1.2 billion maternity clothing biz, Lange's in demand with new moms. Once an exclusive label with revenues of $8 million, her firm is growing fast, thanks to licensing and distribution deals with Nike and Target.

THE TOP 10 INNOVATORS It's not all about the money. These innovators have challenged conventional thinking by devising new ideas, new ways of working with materials, or new ways of solving problems.

ANGELA BELCHER, 36 Co-founder, Semzyme The nanotechie and MIT prof has a vision for viruses. She's created a way to grow Saran Wrap--like material that can make smaller computer chips or one day store vaccines without refrigeration.

MIGUEL DE ICAZA, 30 CTO, Novell Ximian The other Linux guy, de Icaza brought a graphical interface to the geeky open source OS. In August, Novell acquired his company, Ximian, and its software for converting new Microsoft Windows programs into Linux.

PAUL KRAJEWSKI, 34 Group Manager, Novel Alloys and Processes Lab at GM To reduce fuel consumption, GM's SUVs needed to lose some weight. Krajewski invented nine technologies to enable greater use of lighter-than-steel aluminum and magnesium.

ETHAN ZUCKERMAN, 30 CTO and Founder, Geekcorps To help conquer the digital divide in the Third World, Zuckerman launched Geekcorps. It sends high-tech volunteers to small businesses in developing countries, tying far-flung startups to the developed world.

KEITH SCHWAB, 34 Senior Physicist, National Security Agency Quantum physicist Schwab is building a monster code-breaking computer for the NSA. In academia, he devised better measurements for Earth's rotation and for tiny nanostructures.

ANDY, 35, and LARRY, 38, WACHOWSKI, Writers, Producers, Directors, The Matrix trilogy Two words: bullet time. The brothers reinvented action movies, taking Hong Kong movie tricks and adapting them for the U.S. The box office for the first two Matrix films: $1.1 billion.

MICHAEL KREMER, 38 Economics Professor, Harvard University MacArthur Award-winner Kremer has created econ-based programs that enable drugmakers to sell vaccines to the Third World at a profit while also making the drugs affordable to those governments.

STEVEN LEVITT, 36 Economics Professor, University of Chicago "Dismal scientist" Levitt's controversial research showed that legalizing abortion lowered future crime rates. He also studies sumo wrestling corruption, cheating, and gang economics.

PAUL DEPODESTA, 30 Assistant General Manager, Oakland A's Baseball vets go by the gut; DePodesta goes by the numbers. He tossed out traditional stats and designed new metrics for measuring performance, allowing the A's to build a top team on a low budget.

HELEN GREINER, 35 President, iRobot Greiner has made robots an everyday commodity. iRobot's Roomba vacuum cleaner sells for only $200, and the Army uses its Packbot for reconnaissance in Afghanistan and Iraq.