Install QGIS in Ubuntu 16.04

Add repository to your /etc/apt/sources.list

Editing source list

Edit using Gnome Editor
sudo gedit /etc/apt/sources.list

or using Nano Editor
sudo nano /etc/apt/sources.list

Insert the following at the bottom of the repository list

deb http://ppa.launchpad.net/ubuntugis/ubuntugis-unstable/ubuntu xenial main

To avoid errors keyserver are needed

sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-key 073D307A618E5811

Update repository

sudo apt-get update

Installing needed libraries and the application

sudo apt-get install qgis python-qgis qgis-plugin-grass

Source: QGIS