Puting Garmin Edge course on Google map

Use Google Earth directly

The short and easy way is to read from the GPS unit directly into Google Earth using the "Tools...GPS" dialog. Do the setup and it imports it directly.

Some other nice tools like SportTracks or TopoFusion provide a lot more capabilities and also support exporting in Google Earth's kml format.

is there a way to transfer files/courses from Garmin training center to google earth?

thanks for the info, after playing around withit for awhile I have managed to get a course to show up. Now I just need to learn what I can do with it.

On the latest versions of training center you can right click your workout -> there is a "View <date of workout> in Google Earth"

I use gpsvisualizer as it looks better -> Right click on workout and export (in training center again)
Then read that file into gpsviualizer.
http://www.gpsvisualizer.com/