After a hiatus, Google ( GOOG) shares seem to have their groove back.

The search giant's stock is trading near new highs and is up about 12% since the company announced second-quarter earnings in July. And the shares are up almost 25% since August lows, which followed a rare profit miss because of aggressive hiring, among other reasons.

Google's gains follow a period of relative stagnation for the stock. Before the latest run, shares traded at around levels the search giant first saw at the end of 2006. Meanwhile, the buzz over the last quarter has ranged from new video ads it introduced to the prospects of the company getting into the mobile phone business.

But it's the company's core search business that has powered gains this quarter. And tweaks that Google made to its ad-displaying algorithm over the quarter have investors expecting that the company may trump its heady expectations.

For the third quarter, analysts surveyed by Thomson Financial expect Google to earn $3.78 a share on revenue of $2.95 billion.

By almost all measures, Google continued to take market share in search over the quarter. It commanded about 64% of the market as of August, according to research firm Hitwise. And of the 61 billion searches conducted globally in August, about 37 billion of them were conducted by Google, research firm ComScore said.

Google also introduced new changes to the way it ranks display ads and the rates it charges to advertising during the quarter. As part of the change, advertisers will now have to pay the highest amount they bid for an ad. Previously, advertisers would get a refund for the amount between what it took to win an ad auction and their bid.

The move is widely expected to boost the amount Google makes on search. And with a continually growing market share, the reach that Google can bring to advertisers continues to increase when compared to rivals. That means there could be yet more ways to boost rates down the line.

"We continue to believe Google maintains a lot of flexibility with regard to monetization and continue to see expansion internationally as a tremendous source of upside for the company," Thomas Weisel analyst Christa Quarles wrote in a research note last week. Thomas Weisel makes a market in Google shares.

Still, while investors are expecting great things from Google's search business, they'll also be listening carefully to the company's strategy to move into new arenas. Given that the company is expected to grow its already massive earnings at clip of 30% annually over the next five years, Google will have to look well beyond search to live up to forecasts.

In that regard, the company's forays into the related display, video, and mobile markets will take center stage.

Investors will be looking for more commentary on the regulatory approval process surrounding Google's proposed takeover of DoubleClick. During the quarter, Microsoft ( MSFT) spearheaded an aggressive campaign to convince legislators that a combined entity would give Google too much power and threaten user privacy.

Google also introduced ads on its YouTube video-sharing service. While the ads are still in a trial stage, the company's indication of how they're performing -- and when they'll start helping earnings -- will be important.

Finally, Google's plans for the mobile arena will be closely scrutinized. Speculation about what the company will do has been rampant, with competing theories speculating whether the company will introduce a handset or limit itself to providing software.

Along with another strong quarter for search, Google will have to deliver some sharp thinking about how it plans to move beyond its core sector if it's to keep the support it has recently won.