STORY PT. 1 (SPOILERS)
In Crysis 3, you play as Prophet, a super soldier equipped with the nano-suit combat armor, a technological marvel built with alien technology that “lives” in symbiosis with its user. The game takes place several years after Crysis 2, in the aftermath of an alien war fought on the streets of Manhattan. The aliens have been defeated, save for a few straggling survivors who without the central leadership of their hive mind, have been reduced to primal beasts wandering the wasteland that used to be the big apple.
The Private Military Company CELL has contained the situation in the city by building a gigantic dome over it called the Liberty Dome; essentially a massive greenhouse. They keep the city secure and closed off from the public, but they aren’t doing this to protect the world from any remaining alien threat; rather, the dome houses the nexus, an immense power plant which draws from alien technology hidden below the city to create unlimited amounts of energy. CELL needs to protect the nexus; they’ve sold its energy to the world at minimal prices, making CELL very rich, and very powerful. CELL now controls the world through their energy monopoly, and only a handful of people are left rebelling against them.
The Liberty Dome
The rebels however, have some impressive allies, including nano-suit creator Karl Ernst Rasch and Psycho, one of the main characters from Crysis 1 (and protagonist of Crysis: Warhead). The rebels have been planning to destroy the nexus and thus strike a critical blow against CELL, but to do that, they need help from Prophet, the only person left who has a nano-suit, thereby making him a priceless asset.
Prophet however, is being held by CELL in a stasis tank in New York’s harbor. While in the tank, Prophet is plagued by visions of an alien leader, the Alpha Ceph, who is still alive and in hiding. If allowed to live, the Alpha Ceph will eventually usher in the end of humanity.
Psycho – Looks almost real, doesn't he? Curiously though, looks nothing like Psycho in Crysis 1
Psycho breaks Prophet out of his containment, and the two manage to sneak into the Liberty Dome, where they are greeted by an unrecognizable and beautiful Manhattan, overtaken by nature: Buildings are covered in vines and trees; deer are walking the streets, and frogs swim in the many rivers and swamplands.
Eventually, the two of them meet up with rebels inside the dome and coordinate an attack to destroy the nexus. Predictably, as the nexus is destroyed, we find out that the Alpha Ceph is the power source that CELL has been using. By destroying nexus, Prophet has released the Alpha! You can pretty much figure out the general direction of the plot from there.