First, install Microsoft's key:
wget -q -O - https://packages.microsoft.com/keys/microsoft.asc | sudo apt-key add -
Then add Microsoft's repository:
sudo sh -c 'echo "deb [arch=amd64] https://packages.microsoft.com/repos/edge stable main" >> /etc/apt/sources.list.d/microsoft-edge-beta.list'
Update software:
sudo apt update
Install:
sudo apt install microsoft-edge-beta