Updated July 31st: read my full review of Prince of Persia here

Sum up:
Prince of Persia retains the same name, platforming, puzzle solving, and combat elements from the previous trilogy, but starts from scratch with the story and characters. The new story revolves around the Prince having just acquired a large amount of treasure and thinking of ways to spend it (preferably on women and drink). But while preoccupied with these thoughts, a sandstorm soon aproaches and overtakes the Prince. When he comes to, he finds himself in a beautiful garden, meets a girl named Elika, and learns that an entity called Ahriman has destroyed the garden's "Tree of Life," resulting in many of the garden's areas being turned to darkness. It's up to you to stop it from spreading.

Unlike previous Prince of Persia games, this includes a free-roaming and non-linear overworld as its main hub and levels, and the Prince has a female companion who can save him from death when he falls, perform a variety of magic in combat, and help him traverse the game's environments. The game's combat system has also received some changes, and instead of fighting multiple enemies at once, the Prince will fight a single enemy at a time, with the actual combat playing out similarly to a fighting game.

Recommended age:
The ESRB rated this game "T" for Teen, listing "Alcohol Reference," "Mild Suggestive Themes" and "Violence." The "Alcohol Reference" will be just that, referrence, meaning the Prince won't drink, you'll only hear mild talk of alcohol. The "Mild Suggestive Themes" will probably consist of mild flirting between the main male and female character, there might be some very mild suggestive dialog, and the female character may be dressed in a somewhat revealing outfit.

The "Violence" will consist of the Prince fighting the game's enemy creatures, and there's sure to be some moderately intense situations in gameplay and cutscenes. So overall, this game will be pretty tame, with no actual red-colored blood, language, or sexual content, and your sole enemies will be monsters. I'd recommend this game for ages 13+.