Seems like every WP theme I can find is centered around blogging. But I do not want a blog. I am trying to create a training site. I would also like this to work well on mobile devices.
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Seems like every WP theme I can find is centered around blogging. But I do not want a blog. I am trying to create a training site. I would also like this to work well on mobile devices.

What do you mean by a "training site"?
Personal training? Instructional workshops? Something else?
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I don't quite get it, what's a training site? Anyway i know a site where you can get some Best Wordpress Themes from. Check it out to see if it got what you need.
Maybe author means the training site as a platform for web design beginner? In this case every simple WP template is suitable.
But if he wants to make a site about fitness, it will be better not to find a free templates but simply order the design and coding.
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