In this new phase, Google’s destiny is no longer just a second act in an American life. Its fortunes and conflicts are being played out on a global stage – not only in the U.S., but famously in China and, to a less well-known degree, Europe. The often overlooked fact is that Google is a truly global company with over half of its revenue from outside the U.S. including at least 12 percent from Britain and another large portion from the rest of Europe. At last count, Google had more offices in Europe than in the U.S. (21 to 19). This year Google is hiring 1,000 new employees in Europe.

Life is not always comfortable in the EU for Google. The fact that Microsoft, long viewed in Brussels as the “great Satan” of digital globalization of all companies, has been able to bring an anti-trust complaint against Google before the Commission is a sign of the new times. Google itself has begun to realize its situation. “When an elephant enters a crystal room,” said Carlo D’Asaro Biondi, the French-Italian head of Google’s southern European operations, “you have to be cautious. And we realize that we’re an elephant now.”

The size of the digital mastodon (and a reason for the European Commission’s non-benign interest) comes from a few statistics: Google has higher market shares in the European search market (90 percent) than in the U.S. (65 percent). The exception is the Czech Republic, where a local competitor has a substantial share.

How Google got to be that elephant is a fascinating chapter of technological innovation and commercial globalization. It is told in fascinating detail (and great length at 424 pages) in best-yet book on Google: “In the Plex,” – a nickname which refers to the company’s headquarters in Mountain View, California dubbed the “Googleplex” -- comes from veteran info-age chronicler Steven Levy (author of the now-classic “The Hackers”), who has benefited from exceptional access to the Google’s executives and innovative engineers and marketeers. Levy’s book is a valuable history of the rapidly fading youthful magic. It takes readers back step by step, product by product, employee by employee, financial leap by financial leap through the history of this remarkable company. Levy received unprecedented access to Google, over a long period. He had over 200 interviews with present and past employees, including multiple long sessions with founders Sergey Brin and Larry Page, along with former CEO Eric Schmidt, who served as CEO for 10 crucial years in Google’s life. Levy was made privy to emails, internal documents and memos, strategy sessions and other inside info never shared with an outside writer. (Notwithstanding Google’s professions of openness and transparency, it is highly secretive, and sometimes arrogant, about the proprietary nature of its product development and other aspects of the company that should be held within the “Google family.”)

Levy’s description of the development of the fabled Google search algorithms are clear and authoritative and never before publicly so well explained. Larry Page, Levy writes, had academic parents so he became aware that web links could be deemed comparable to citations in scholarly articles and that one could identify which papers were really important simply by tallying how many other papers cited them in their own notes and bibliographies. Tallying up the links on the Internet could provide the same insight, Page concluded. In a stroke of genius, he figured out that by working back and cataloging in a data base which links were connected to which sites, one could provide the basis for a valuable step forward in search methodology. “PageRank”, a sly vanity since the reference to “Page” may be to Page himself as well as to as most assumed, to web pages.

This methodology refined and augmented with other tools and “signals” made Google into the better mouse-trap in the search world. Also crucial was Sergey Brin’s ability to apply complicated math to the database compilations to produce the “PageRank” results. The results were astoundingly good even at the beginning of google.com, when the company was operating with only two computers — one for search and one for everything else. On the computer used for search there was a giant chain of disk drives that stored 25 million web pages.

The scale-up to current day is carefully chronicled, although even Levy was not able to confirm the exact dimensions of Google’s massive digital infrastructure, which Levy says is Google’s most closely held secret. Based on industry reports Levy estimates that as of 2009, Google had 24 major facilities around the world with an unspecified number of servers (probably numbering in the hundreds of thousands). Google did tell Levy that it is the largest computer manufacturer in the world. Making its own servers requires it to build more units every year than industry giants, HP, Dell and Lenovo.

Levy was able to confirm, sort of, how much it cost Google to provide gourmet food to its employees. While Brin would say only that the cost was “less than a rounding error,” the director of Google’s human resources appeared to confirm $17 per day per employee or about $80 million a year for free food.

From details like these, Levy offers a particularly rich chapter on Google’s experience in China – where Google was involved in a dispute with the authorities about whether it would censor its search service. It was a test case of Google’s own much-vaunted commitment to openness (Brin himself was especially sensitive about the issue because of his Russian family background). In China, Google grew fast, with its Chinese-language service gaining an estimated 25 percent market share by 2002, only two years after it started. But there were episodes when Google was entirely blocked in China and then mysteriously reinstated. In the meantime, the Chinese search engine “Baidu” increased its leading position. As a condition for operating in China, Google agreed to censor searches according to government instructions to prohibit access to subjects like “Tiananmen Square” – a concession that many observers found hard to square with “don’t be evil.” But the decision to go forward in China was based on the theory that Google, even a censored Google, would do more good in China than harm.

That view was reversed in 2009 when censorship became more obtrusive and Google databases were hacked by a sophisticated hacker widely believed to be the government. In a decision that was apparently opposed by Schmidt (who had been brought in to provide “adult supervision” for Google’s entrepreneurial founders) Google abandoned its Chinese venture. (Levy speculates that this may have caused a breach with the founders, especially Brin, who contributed to Schmidt’s departure.)

The China incident was one growing-up episode. Another, chronicled in painful detail by Levy, is Google’s failure in the social networking world and the emergence of a more personal business model ethic espoused by Facebook in contrast to Google’s engineering and data-based rigidity.

And there is the long-running saga of Google trying to apply its vision in the Google Book Search project – an undertaking in which the founders have sought to overcome every obstacle and objection to their dream of digitally scanning the estimated 33 million books printed since Gutenberg invented the moveable-type press. Page and Brin continue to be mystified by the hornets’ since, in their view, the ambition to preserve the world’s printed corpus should be welcomed as an historic good.

The negative reaction was particularly strong from some quarters in Europe, especially in France, where cultural leaders warned that the idea of an American firm, however well intentioned, could produce an “American filter” on access to a global library and thus penalize French and other smaller cultures. Others in Europe have welcomed the Google effort on the grounds that only Google had the will and assets to pursue the project.

Google has become more sensitive to the issues raised by its books project and has signed agreements in France and seven other countries to give artists and copyright holders a cut of revenues from material on YouTube and Books. And it presses forward, with some 15 million books scanned as of October 2010. Meanwhile, a related case brought against Google in the U.S. seems to be stuck in litigation.

As “In the Plex” closes, it is clear that both Brin and Page must be realizing that it is very difficult to be as big and influential as Google has become without putting some intractable pressures on its founding mantra “don’t be evil.”

William Marmon is Managing Editor of “European Affairs.”