I have tried to avoid spoilers for those who have not yet played, I still don't recommend reading if you have not played the game.
Bioshock Infinite is bold, very bold. This addition takes a much needed leap from the series, jumping straight into a prequel that does an excellent job at not feeling rehashed and copy paste. You play as a man with a heavy heart by the name of Booker Dewitt. Booker is numb to violence, and numb in the heart. Booker is in debt, when he is visited with the offer of clearing his debt, for one thing, a girl named Elizabeth. "Bring us the girl and wipe away the debt". This brings Booker to Columbia, a floating city in the sky. This is one of Infinite's greatest strengths, it's stylized graphics and beauty touch close to the heart. It immerses you not through realism but beauty, it's plastic like, yet detailed graphics are very much attractive throughout the game and helps create jaw dropping moments that aren't soon forgotten.The city of Columbia in of itself is a graphical astonishment, it floats upon clouds, maintaining a bright early 20th century feel. Exploring this city is enough to open your mind, at the same time displaying extremely early themes and ideals. This can vary from extreme use of religion and racism.
The game play on the other hand is not so great, the game gives you three basic ways of attack, your gun, your skyhook melee attack, and vigors. The gun play is fairly generic and weak, although the guns are interesting using them is fairly uninteresting and generic, it's not until you combine it with your vigors that make it any bit satisfying. The vigors are nicely varied but I find myself finding the need to change vigors very sparse. They are very interesting but they feel under utilized, and not very important to the game play, for example you could get through the whole game without using any vigors, making them that mechanic where you say "Oh, yeah! I can do that." On the other hand the skyhook is well used and well integrated, it can be used as a melee move which also packs a brutal finishing move but it's main mechanic is travel. You can travel through the use of sky lines, these skylines are usually in linear areas used to travel to other nearby areas, but it also creates an interesting game play style. You jump onto these sky lines and start to travel along it, in which you have access to your gun, you can shoot your gun or jump onto opponents to take out a good chunk of their health. What's so special about this is it creates a fast paced addition to the game. You can for example jump onto a skyline shoot enemies as your riding it, jump onto them, and them shoot the nearby enemies. This creates the most enjoyable parts of the game but not these parts are not as common as they should be.
Elizabeth, a character that will follow you throughout most of the game. That has to be a disaster, right? No, not at all, this is pulled off very well. She is actually useful, not only that but she can't die, keeping her from being a nuisance. She stays useful by throwing you health when you are close to dieing, throwing you ammo when you're low, and salts when you need to use your vigors. She can't do this constantly throughout a battle, though, because she searches for it. This keeps it from being easy but at the same time making her useful. She can also pick locks to help you advance and can occasionally find some money to spend at nearby vending machines, containing ammo, gun upgrades, and vigor upgrades.
The main draw of this game is not the game play, though. It's the story, and damn... This game pulls it off. There's not much to say without spoiling it but what I can say is it's good. The game uses many elements, one notable element is time travel, yes time travel. Not only this but alternate universes. Elizabeth, who is being held in a tower throughout her life by the "Prophet" Father Comstock. Booker Dewitt, a former agent for a man by the name of Pinkerton is sent to get Elizabeth to wipe away his debt. When he arrives in Columbia he finds that he is received to as the "False Shepherd" causing him to be sought after as a criminal. Finding Elizabeth he finds she has the ability to open tears, alternate universes in alternate times that she can enter and take things out of. Using this base, Irrational games has created a game that has a story that will be remembered for years to come. If you came here to see if Infinite is a good game, it is. So much so it's hard not to say it's perfect, but it's not, but it's good enough to say it probably won't be topped for a while.