The proper way to do the installation is through PPA. So copy/paste these lines in the terminal and it is installed.
This installation is a bit more specific because of line 2.

sudo apt-add-repository "deb http://repository.spotify.com stable non-free" 
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys D2C19886 
sudo apt-get update 
sudo apt-get install spotify-client

linux-mint-17.3-spotify