There are only a few templates (see image) but you can tweak any one of them to your own requirements in the right-hand panel and then save the settings as your own user template.
There are more templates available for web galleries including HTML5 templates but you need to have a website that can host them.
Thanks for responding...the problem is I don't have those available. I've checked and rechecked...they are definitely not there. Any suggestions?
In the Slideshow module go to the menu bar and click:
Window >> Panels
Make sure you have all panels selected including the Template Browser
It's working now...and I thank you so much for al of your help! That must have been the problem.
I have a very similar problem since upgrading from LR5.6 to LR6 but the action recommended above unfortunately does not resolve it.
The slideshow Template Browser is visible and below it are 'Lightroom templates' and 'User templates' but clicking on Lightroom Templates does nothing - no list of templates appears. Strangely, the Template Browser shows regardless of whether Window>Panels>Template Browser is ticked or not. However, if I right-click on the Template Browser itself I can deselect it there.
I have checked that the slideshow templates folder is present (Program files>Adobe>Adobe Lightroom>Templates>Layout templates>templates_slideshows). It's a 370KB folder.
I can't find a way round this - does anyone have any ideas please?
I posted my question back in Sept 2015 and never did resolve the issue despite trying everything I could think of including reinstalling LR6.1. Today I installed Lightroom 6.4 and guess what? - problem solved. Everything in the slideshow module works exactly as it should. Why? - goodness knows, but I'm just relieved that it does