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wich consists of a listing of scholars around the left and lots of abilities to assign to every student.

Each student have it´s own table using the full skill list (HTML, CSS, ...). Now what is an easy method of getting value in the checkboxes and assign these to the related student table?

The reason would be to developing a graph for every student showing their skillset :-) ah, sorry for my poor british.

Print the shape utilizing a scripting language like PHP. Make use of a wise naming for checkboxes, then place the logic to retrieve data within the script that get the publish form.

If you are using php, u may use

<form>
    <input type="checkbox" name="paul[skill1]" value=1>
    <input type="checkbox" name="paul[skill2]" value=1>
    ...
    <input type="checkbox" name="robert[skill1]" value=1>
    <input type="checkbox" name="robert[skill2]" value=1>
    ...
</form>

when posting the page, the $_Publish result is going to be

$POST = array(
  [paul]   = array( [skill1]=> 1, [skill3]=>1) //paul has skills 1 and 3
  [robert] = array( [skill1]=> 1, [skill4]=>1) //paul has skills 1 and 4
)

if you wish to get it done everything around the frontend, you need to use JQuery, but than controlling data it's harder. I guess you've PHP abilities, otherwise make use of a Spreadsheet to get this done