SQL date format convert? [dd.mm.yy to YYYY-MM-DD]

Since your input is a string in the form 03.09.13, I'll assume (since today is September 3, 2013) that it's dd.mm.yy. You can convert it to a date using STR_TO_DATE:

STR_TO_DATE(myVal, '%d.%m.%y')

Then you can format it back to a string using DATE_FORMAT:

DATE_FORMAT(STR_TO_DATE(myVal, '%d.%m.%y'), '%Y-%m-%d')

Note that the year is %y (lowercase "y") in STR_TO_DATE and %Y (uppercase "Y") in DATE_FORMAT. The lowercase version is for two-digit years and the uppercase is for four-digit years.

Use

SELECT CONCAT(
'20',
SUBSTR('03.09.13', 7, 2),
'-',
SUBSTR('03.09.13', 4, 2),
'-',
SUBSTR('03.09.13', 1, 2))

Fiddle demo.

More about formats you can read in the corresponding manual page. Tip: if this is about conversion value from non-datetime field - better to use DATE/DATETIME data type instead. However, this is a bad idea to operate with dates via string functions. Above there is a nice trick with STR_TO_DATE (will not repeat that code, updated to fit better)

Dates are stored using an internal format. You can use the function date_format() to convert it to a string using a variety of formats. For yours in particular:

select date_format(`date`, '%Y-%m-%d')