When I first saw this game, I thought this is an adult game. After playing the game itself, I found myself that I was wrong, and this game is far than an adult game. It teaches a lot of things to people, especially about love.
Story
Gameplay
You have the option to Retry the stage from the beginning or from a checkpoint. However, the number of Retries are lesser in harder difficulty modes, whereas more Retries in easier difficulty modes. The different difficulty modes also affects the difficulty of every stages in the game. If you think the current difficulty is too hard, you can always change it during playing. Please be noted that the number of Retries carries over throughout the game, not in that particular level or sub-levels.
Each stages have items that can help you to complete a stage faster, such as an item that creates anew block, items that increase your number of Retries, items that allow you to change all blocks to Normal Blocks, etc. It is useful to get these items, as it can help you to escape from a tight spot.
Story

There are two Catherines in this game, but one is spelled as Catherine, while the other is spelled as Katherine.
The game stars Vincent Brooks, who is a man that always spends his time at the bar called Stray Sheep with his friends after working. One night, he met a beautiful girl by the name of Catherine, coincidentally same name as his girlfriend, Katherine, albeit in different spelling. On that particular night, he slept with Catherine, and he started to have weird nightmares of climbing walls of blocks. Should he dies in the nightmare, he will die in real life. In the following days, Vincent have to make a choice of choosing Catherine or Katherine as his beloved one.
The characters are incredibly well developed, both main and supporting characters. All of the characters in the game deserves their spotlights, having their own dilemmas about love, guilt, and many other problems. Vincent in particular, is troubled due to his affair with another girl, and it is interesting to see his reactions and thoughts in the game.
The game's story is very interesting, unique, and bizarre. Nothing less than I expected from the team that makes the popular newer Persona games. It has great plot twists, addicting story telling, and great characters to back up the story up.
Gameplay

Don't be mislead by the moving blocks puzzle gameplay. It is addicting, but the difficulty is really hard even in Normal mode.
The game is both puzzle platformer and adventure.In most times, you will spend most time to play the puzzle levels in Nightmare mode. Each levels have several sub-levels, and they are different for every new levels.
Your main objective in the Nightmare levels is to reach the top in every stages. In order to do so, you need to climb up blocks and move to the top of the stage. If you are unable to reach the top, you can always create new footings by moving blocks front, back or on top of a block. This will be a key technique for you to traverse each stages safely.

Fighting bosses are not like it looks like. You have to evade the boss's attacks while climbing up the wall of blocks.
During the final sub-level of a level, you have to fight a boss. They can impede you from progressing in the final stage of a sub-level, so you have to think creatively to climb up the blocks fast while evading their attacks.
You have the option to Retry the stage from the beginning or from a checkpoint. However, the number of Retries are lesser in harder difficulty modes, whereas more Retries in easier difficulty modes. The different difficulty modes also affects the difficulty of every stages in the game. If you think the current difficulty is too hard, you can always change it during playing. Please be noted that the number of Retries carries over throughout the game, not in that particular level or sub-levels.
Each stages have items that can help you to complete a stage faster, such as an item that creates anew block, items that increase your number of Retries, items that allow you to change all blocks to Normal Blocks, etc. It is useful to get these items, as it can help you to escape from a tight spot.

There are a variety of Blocks used in every levels, such as Bomb Blocks, Trap Blocks, Dark Blocks, etc.
Not only you can push and pull a block, you can do hanging to climb vertically of the blocks. This allows you to get through hard areas, as well as escaping boss' attacks. Sometimes while playing a sub-level, there are other sheep that can attack you. In later stages, they can kill you, but in earlier levels, they don't and just simply knock you down. You can also shove them down by running towards them.
After completing a sub-level, your score will be ranked. The faster and more perfect your climbing in a sub-level, you can get high score and get a Gold prize. It is not really important, but unlocking enough Gold prizes will unlock newer and more challenging levels called Babel.

Learning new block techniques will help you to get through the game easily.
After completing a sub-level, you will go into a safe spot where you can save your game and talk to other sheep. Talking to the sheep can help motivate them to climb further, get new techniques, solving their dilemmas, or buy items. It is highly advisable that you choose carefully when talking to sheep that are having dilemmas, as it can affect your Alignment bar.
The Alignment bar is important as it will affect the game's story, and especially the ending(s) after completing the game. If your Alignment pointer is aligned to the left, it means you are favouring chaos, freedom, etc. Particularly, this means that you are particularly more interested with Catherine herself. If the Alignment pointer is aligned to the right, that means you are favouring discipline, good, loyalty, etc. This means that you are particularly loyal with Katherine, Vincent's girlfriend. The Alignment bar also affects the game's cutscenes, as it will affects Vincent's thoughts and morality in the game itself.

Talking to the sheep during Nightmare and the people in Daytime is a part of the game, and very important to do so.
During the Daytime mode, you can also do side quests of solving the customers at the bar dilemmas by talking to them and choosing the correct responses. By doing so, they are motivated, and will remain alive until the end of game. If you do not do that, they will end up dead, unable to interact for the rest of the game. It is advised to do so, as a number of them will teach you useful techniques in the Nightmare stages.
Drinking beers, cocktails, etc during Daytime mode is useful, as it increases Vincent's running speed in the Nightmare levels. During the Daytime mode, you will mostly watching a plenty of cutscenes that are integral to the game's story itself. You can also skip them if you want, but the cutscenes are definitely worth watching repeatedly. You will also receive text messages via your phone, where you can reply with. Some text messages also grant you the chance to increase your Alignment to your current favoured alignment by choosing the correct replies to the messages.
I love the gameplay of this game. It is simply great, addicting, and awesome. The only complaint is that the game's Normal difficulty can be too hard for some players. However, this is easily remedied by choosing the Easy mode, or the secret Very Easy mode. These modes are meant for players who want to enjoy the game's story, not the challenges of hte puzzles. Personally, I enjoyed the game like LittleBigPlanet, but Catherine is my personal favourite because it has a great story, whereas LittleBigPlanet does not.