The world's fourth-largest cat species
I've seen tracks, but not the actual animal, despite having explored wilderness areas where they live all my life. A friend is certain one growled at him when biking in the Santa Ana Mountains in Southern California. He didn’t bother to look for it, and bolted on his bike.
A man who I spoke with, owner of an orchard and reservoir in the Santa Ana Mountains, told me about a female mountain lion who walked past a certain area every morning at the same time. He would silently watch her go by.
These large cats are slightly larger than leopards. Of all cat species, only tigers, lions, and jaguars are larger. In the Americas, only jaguars are larger.
Also called cougars or pumas, they live nearly everywhere through North America, Central America, and South America. They live in jungles, mountains, deserts, and any climate except extreme cold, such as in the northernmost parts of Canada and Alaska.
They are rare, and quite shy around humans. You'd be incredibly lucky to see one. They have attacked humans at times, but this would be a far rarer event than even seeing one. It’s extremely uncommon.
They'll take down deer, elk, moose, cattle, horses, bighorn sheep, and many large mammals. Like most predators, they’ll go for young, or for any that are sick or old and make easier targets before risking going after a bigger, stronger animal that is capable of fighting back. 
To give you an idea of the rarity of being killed by one, just sixteen people are known to have been killed by them since 1970 in all countries that have them. Of those, two occurred in Southern California, which is where I live. We have millions of people and cities right up against wilderness areas, and still in over four decades there’s been only two fatalities from these powerful predators.
A neighbor of mine once saw a mountain lion in his backyard, in the 1980s. In 2013, a neighbor saw one in a park down the street. However, they are almost never seen amongst houses, since they want to avoid people. But they are around.
They are incredible leapers. Let’s say you have a house with a balcony on the second floor. One would easily be able to jump up onto the balcony.
This is what a paw print of a mountain lion looks like. A large adult has paws similar in size to the palm of an adult human's hand. Smaller versions could be other cat species - such as a bobcat. If you see obvious claw marks at the end of each toe, it is not a mountain lion or any species of cat. Cats keep their claws retracted when walking along, with the exception of cheetahs. Where I live, I often see prints with claw marks that are obviously a dog or coyote, although I have seen actual mountain lion tracks on rare occasions.
Tips for an encounter with a mountain lion:
1. Stay calm and don’t run. They have an instinct to go after and tackle running prey. They can run over 45 mph (72 kilometers per hour), so there is no chance you could outrun them.
2. Don’t get any closer. Mountain lions don’t want confrontations with humans, but will defend themselves if they think you’re being threatening.
3. Make eye contact. This is a bad idea with black bears, but it’s important for facing a mountain lion. Back away slowly while maintaining eye contact.
4. If you have small children, pick them up. Also, avoid crouching or bending over. The taller a person is, the less likely they’ll recognize the person as prey.
5. If they appear to be threatening or getting closer, you can raise your arms to look even bigger or open your jacket wide. If that doesn't work, throw rocks or sticks or whatever you've got at it. The point is to convince them that you’re not worth attacking. They don’t want to get hurt.
6. If all else fails, fight back with everything you've got. One man I read about hit a mountain lion in the head with a rock, after it jumped on his son. It departed, and his son survived.
7. Let others in the area know, especially if they have any children with them. Seek to notify rangers, local police, or whoever is around.
One reason mountain lions are not often seen is because they prefer to hunt at night. Cats have night vision about six times better than humans.