For those starting to learn MySQL and want to install it on a Raspberry Pi: there is a little gotcha you should be aware of.
Disclaimer: Only run command if you know what it does. Always make sure you have backups of your important data.
First you need to put the official Raspbian image on your SD card and then boot the Raspberry Pi.
Then if you try to install mysql with "sudo apt-get install mysql-server-5.5" this will fail. The reason for this is that the filesystem on the SD card will become full. This can be seen by running the "df -h" command.
The SD card is probably 4GB. The filesystem will be around 1.9GB. This was done to make it fit on 2GB cards. To stretch the filesystem to complete 4GB you need to run "sudo raspi-config" and choose the "expand_rootfs" option. Then you need to reboot.
Now "df -h" should tell you that the filesystem has much more free space.
But your MySQL installation failed. So you run "sudo apt-get purge mysql-server-5.5" and remove the mysql-server-5.5 package and all related files.
If you would try to reinstall MySQL with "sudo apt-get install mysql-server-5.5" it would fail again. This is due to the data in /var/lib/mysql which belongs to the failed installation. You should remove that data "rm -rf /var/lib/mysql" and then install mysql again "sudo apt-get install mysql-server-5.5".
Now you should have a basic MySQL installation. You could use the "mysql_secure_installation" command to secure your installation.