"There are animals on the mountain."
To those asking why に is followed by は i will paraphrase an excellent answer i saw earlier:
Dont think of は as the subject marker. Rather, the topic marker. に is still correct usage for "on the mountain" (山に) but by putting the は after, it becomes the topic.
It would be a slightly different sentence if the は was used for どうぶつ because it would be something like this: "there are animals on the mountain" vs "the mountain has animals on it". An ever so slight difference.
i think this question has a wrong answer, why "ni" will followed by a "wa" while? there is no subject in front of "wa".
Some particles can "stack" like this. Someone explained it to me once as meaning that the "は" points to "山に" (on the mountain) as the subject. So it means "As for on the mountain, there are animals." (As awkward as that sounds)
It's because animals are ON the mountain, and the theme is "on the mountain", not just "mountain".
This course translates both 山に and 山の中に as "on the mountain." It really needs to differentiate them in English.
My guess is that your sentence would make the animals the subject, as in "the animals are on the/a mountain"?
"山にはどうぶつがいます。" and "山にどうぶつがいます。" both sentence are correct and have more or less the same meaning. What exactly is the difference? Can this difference get lost by a translation into a natural English?