I am trying to integrate Leaflet (http://leafletjs.com/index.html)

I just copy-and-paste'd the very first demo code but it only displays a gray map..

Here is my code:

<html>
<head>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script src="http://cdn.leafletjs.com/leaflet-0.7.3/leaflet.js"></script>
<link rel="stylesheet" href="http://cdn.leafletjs.com/leaflet-0.7.3/leaflet.css" />
</head>
<body>
<div id='map'>
<script>
var map = $('#map');
map.css('height', 375);
map.css('width', 500);
var map2 = L.map('map').setView([51.505, -0.09], 13);
</script>
</body>
</html>

What is wrong with my code??