This game is a nice addition to the Professor Layton series, though I wouldn't recommend buying this version. If you want to know why, skip to the last paragraph. The game is set before the previous games in the series and deals with how Luke met Professor Layton for the first time.
As always the story is insane and the animation is beautiful and fluid, making the cut-scenes one of the prettiest on the DS, though they often last less than a minute at a time, making it hard to enjoy them. The voice acting, when the voices are used, is superb, with Professor Layton sounding at his most gentlemany and the supporting cast don't have an annoying voice between them.
Gameplay-wise, this game follows the previous games' examples of having random people throw riddles at you and demand that you solve them before they either let you pass or tell you some vital info. While you're left wondering why these people don't ask for something more valuable, like money or sweets, the people will wait patently while you solve their riddle and will compliment you on your quick solution, even if it took you twenty guesses and all of your hint coins.
This brings me onto my next point, hint coins. As in previous games, this game gives the player 'hint coins' to spend on hints to the answer of any riddle you're faced with. Each riddle that you're given has three hints, each of which cost one hint coin and give you a suggestion on how to solve the riddle, and a super hint, which costs two hint coins and basically tells you how to solve the riddle. This all sounds nice and fair until you start playing and realise that the hint coins are everywhere. I wasn't even trying and I managed to find over 150 hint coins by the end of the game; if you were compare this to the original game, 'Professor Layton and the Curious Village', where I had to really search to find 100, this game comes across as much easier.
Storywise, this game is slightly below the previous games' standard in my opinion. Unlike the previous games, this game has no moment which made my mouth drop open and my eyes widen while Professor Layton something amazing happens on screen. 'The Curious Village' has a scene in which Layton make a glider from a pair of curtains and another where he and Luke escape from a runaway Ferris wheel, 'Pandora's Box' has a scene in which Layton has a sword fight with a suspected vampire and 'The Lost Future' has a scene in which he flies a converted version of his own car up to a giant robot that's destroying London. This game does have a fight scene towards the end, but it doesn't involve Layton and has a disappointing ending. However, this isn't a reason not to buy the game and I would've suggested buying it anyway if it wasn't for a rather large problem.
This problem is the reason I suggest NOT BUYING THIS GAME. When released in Japan, the player could unlock another game called 'Professor Layton's London Life'; the American version also has this game, though the player could play it straight away. 'Professor Layton's London Life' is a role playing game which is set in 'Little London'. The player creates a personal avatar and helps the the city folk with their problems. It was advertised to have over 100 hours of gameplay. I wish I could say whether or not this is true, but this version, the PAL version, does not include this other game. This is why I suggest, if you're planning on buying this game, forking out a bit more for P+P and purchase the American version instead, which is called 'Professor Layton and the Last Specter'.