Install GNOME Desktop Ubuntu 15.04

Solution 1:

Log out and open a terminal on TTY1 Ctrl+Alt+F1 and run the following commands:

sudo apt-get install ubuntu-gnome-desktop
sudo service gdm restart

As @Exocom said, the following step is not necessary.

sudo dpkg-reconfigure gdm

Then choose the desktop you want and you can log in again.

Solution 2:

Open a terminal and execute:

sudo apt-get install gnome

Choose "gdm" when asked.

In case not being asked execute :

sudo dpkg-reconfigure gdm  

To restart the system execute :

sudo reboot

Rebooting after installing a new DE is not necessary, however some say it is recommended.

Update :

To make up your own mind on this topic, read When is it necessary to reboot an Ubuntu system?