According to numbers released by Gartner on Friday, Apple is now the third largest smartphone maker in the world and the second largest in the U.S.

Smartphone sales have constantly been going up. In this year’s first quarter, around 32.2 million units were sold worldwide, thus showing a 29% increase when comparing the results with the same period of last year. The U.S. market represents a special case, as it had a 106% growth, with sales of more than 7.3 million units.

Globally, Nokia came in first with 14.6 million units (45.2% market share). A rather distant second place went to Research In Motion (RIM) with 4.3 million units (13.4% market share) and the chart closes with Apple’s 1.7 million sold units (5.3% market share).

These results leave room for great optimism regarding what’s ahead, as Nokia managed to grow its sales by 25.3% and RIM by no less than 107.3% (compared to Q1 2007).

Apple has recently launched or it’s preparing to launch the iPhone in a bunch of new locations: in Japan through Softbank Corp., in Sweden, Norway, Denmark, Finland, Lithuania, Latvia and Estonia through TeliaSonera, in Singapore through SingTel and also several European countries will be taken on by Orange.

China Mobile, with its more than 384 million customers, is also on Apple’s "To Do" list.