Mountain hiking

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I've read that all bears except black bears will only defend themselves if threatened and don't consider you prey. So if you see one, back away. If it charges for you you should: 1) stand your ground no matter what 2) make yourself as tall as possible (waving your arms over your head is also recommended) and make low-pitched noises. If it hesitates, run after it and it will probably leave you alone. If it is prepared to fight, land a good punch in its face or kick it and it will probably retreat. Bears are incredibly strong though so make sure you don't get hit first as you can easily be knocked down.

For wolves, I've read that you should avoid direct eye contact, make yourself as tall as possible (with the arms like I mentioned above) and move towards solid ground. I don't know what the significance of solid ground is but I've read that wolves will not follow you if you move onto solid ground like rock (have no idea why). If it's a stray wild wolf then you can use the bluff method described above but wolves that are used to the presence of humans will not be scared and will probably not retreat. They are essentially dogs though which means if you can seriously injure them they will flee. They can leap large distances and are much stronger than normal dogs though so this will probably be difficult. Overall I'd say avoid going off the designated path if there is one and if you see a dangerous animal from afar go in the other direction.