Here are the instructions to installing Docker CE on Linux Mint 18.1 Serena.
sudo apt-get install apt-transport-https ca-certificates curl software-properties-common
curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo apt-key add -
The following line in the SOURCE automatically determines the distribution, which is Serena, but there are no Linux Mint packages for Docker. You have to change it to the matching Ubuntu distribution. FYI Linux Mint Serena is based on Ubuntu 16.04 Xenial.
sudo add-apt-repository "deb [arch=amd64] https://download.docker.com/linux/ubuntu xenial stable"
sudo apt-get update
sudo apt-get install docker-ce
Test the Docker install with this command. It will automatically download the hello-world image and run it.
sudo docker run hello-world