If you come across running out disk space below:
“The upgrade needs a total of 25.3 M free space on disk `/boot`.
Please free at least an additional 25.3 M of disk space on `/boot`.
Empty your trash and remove temporary packages of former installations”

$ sudo apt-get clean.

You can run the following
# to see available space

$ df -h

# to see the current kernel in use

$ uname -a

# to list all the current stored images

$ dpkg -l | grep linux-image

check that the ones you want to delete is not your current running kernel.
# to delete images you can run:

$ sudo apt-get purge linux-image-extra-3.13.0-{51,52,53}-generic

# where {51,52,53} are the images you want to delete
# note! make sure that you do not delete your current image.