My cousin, D. used to work in a National Park and had an international intern worker C. who decided to walk to work every morning through the park. D. had warned her to be cautious of mountain lions in that area. One morning D. was driving to work and saw her walking and not very far behind her a mountain lion making a 'stalk' approach and D. was able to get her attention and direct her attention to the mountain lion. C. hurried to D's car to ride the rest of the way to work and decided to accept the standing offer or a ride to work.
If you choose to trail run in mountain lion country, a bell may scare off bears, but may have the opposite effect for mountain lions. Stay aware, don't wear headphones or zone out on the trail.
I have seen three separate stalk and harvest events, the cow elk was my first and closest. My second was a wild burro colt. The the third was an old javelina (collared peccary). The second was by far the scariest, as the puma actually bit over the mouth and nose of the colt and suffocated it.
Fear is the correct emotion with regards to these wild animals. If you want to see one, the Arizona Sonora Desert Museum (really a zoo, in spite of the name) is the best and safest way I know about. I would never willingly try to find one in the wild unless i had a hunting permit for one, and I'm not inclined to do that.