Google Map: Uncaught ReferenceError: google is not defined

I'm working on a google map script which is throwing up this error. The issue is in this line:

var map = new google.maps.Map(document.getElementById('google-map'), {

Corresponding HTML snippet is:

<!-- Google Maps -->
    <div id="google-map"></div>

I've seen few questions which propose solutions to this problem but I havent really understood most of them: asynchronously loading the script or having a developer API key.
I'm just looking for a solution to what the issue really is and preferably a logical explanation to what the problem is.

Edit 1: The link the API is missing. I have added that and the error has gone but still the map doesnt show up. ( Please note that I've used PHP to divide the code into segments. )

Solution

I ran your script, and it seems like the following error is very common.

Uncaught TypeError: Cannot read property 'offsetWidth' of null

I found this question: Google MAP API Uncaught TypeError: Cannot read property 'offsetWidth' of null with answers suggesting that the error is because of not rendering the map div before the js script runs.

Try:

<script>
/* Your location */
function initialize () {
    var locations = [
        ['IIIT Hyderabad, Gachibowli, Hyderabad <span>Head Office</span>', 17.444792, 78.348310, 1]
    ];

    /* Map initialize */
    var mapCanvas = document.getElementById('google-map');
    var mapOptions = {
        zoom: 10,
        center: new google.maps.LatLng(17.444792, 78.348310),
        panControl: false,
        zoomControl: true,
        scaleControl: false,
        mapTypeControl: false,
        mapTypeId: google.maps.MapTypeId.ROADMAP
        }
    var map = new google.maps.Map(mapCanvas, mapOptions);
    }

google.maps.event.addDomListener(window, 'load', initialize);
</script>

This only calls the script after the page has loaded. I ran it and it works for me.