func keyboardWillShow is not called. It seems an issue with communication via notifications.

import UIKit

class ViewController: UIViewController, UITextFieldDelegate {

    enum Error: ErrorType {
        case NoName
    }
    @IBOutlet weak var nameTextField: UITextField!

    @IBOutlet weak var textFieldBottomConstraint: NSLayoutConstraint!

    override func viewDidLoad() {
        super.viewDidLoad()

        // THE MISTAKE MIGHT BE HERE I SUPPOSE
        NSNotificationCenter.defaultCenter().addObserver(self, selector: Selector("keyboardWillShow"), name: UIKeyboardWillShowNotification, object: nil)
    }

    override func didReceiveMemoryWarning() {
        super.didReceiveMemoryWarning()
    }

    override func prepareForSegue(segue: UIStoryboardSegue, sender: AnyObject?) {
        if segue.identifier == "startAdventure" {
            do {
                if let name = nameTextField.text {
                    if name == "" {
                        throw Error.NoName
                    }
                    if let pageController = segue.destinationViewController as? PageController {
                        pageController.page = Adventure.story(name)
                    }

                }
            } catch Error.NoName {
                let alertController = UIAlertController(title: "Name Not Provided", message: "Provide a name to start your history!", preferredStyle: .Alert)
                let action = UIAlertAction(title: "OK", style: .Default, handler: nil)
                alertController.addAction(action)

                presentViewController(alertController, animated: true, completion: nil)
            } catch let error {
                fatalError("\(error)")
            }
        }
    }

    func keyboardWillShow(notification: NSNotification) {
        print("keyboard will show")
    }

}