The problem lies in your jQuery code
1. Missing closing
</script>
in the jQuery library
2. Put your jQuery code in document.ready function so that they are effective only after the loading of the whole page
3. The names of the selectors should prefix with # since they are name as id in the body.
See the corrected jQuery code:
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script>
$(document).ready(function(){
$('#Panel1').hide();
$('#Button1').mouseover(function () {
$('#Panel1').hide();
});
$('#Button1').mouseout(function () {
$('#Panel1').show();
});
});
</script>