I recently had to upgrade MySQL to 5.6 but found that Debian provides MySQL server 5.5 with both Jessie (v8) but the latest GA releases are 5.6 and 5.7 with some enhancements and added features, including support for InnoDB Full-text search.
So to install the latest version on Debian do this:
1. Download the MySQL APT repository config tool (you can see more details here: http://dev.mysql.com/downloads/repo/apt/)
2. Install the MySQL APT repository config tool
dpkg -i mysql-apt-config_0.7.3-1_all.deb
3. If you get an invalid key error run:
sudo apt-key adv --keyserver pgp.mit.edu --recv-keys A4A9406876FCBD3C456770C88C718D3B5072E1F5
You will be asked to select product and version that you want to install. In the first step, select Server and next select either mysql-5.6 or mysql-5.7. Then click Apply.
3. Update APT
4. Install the server
apt-get install mysql-community-server