I'm from rural CA and in almost three decades of exploring the woods/mountains I see mountain lions fairly often (And I'm sure many, many more saw me when I didn't see them!). Mountain lions very rarely attack humans. Usually when they do it's for one of two reasons: (1) they feel threatened by the human or (2) they confuse the human for its usual prey.

Because of this, you should never ever approach or try to touch a mountain lion. Especially if the mountain lion has cubs. So when you see a mountain lion you should turn tail and run, right? Wrong! Running can fire up their predatory instincts and they are much faster than you. Never ever run from a big cat. You should also never lie down, squat, sit, kneel, etc. They almost never attack bipeds but they could mistake you for some weird quadruped forest animal if you are hunched/prone/etc. It also goes without saying children and dogs are much more likely to be attacked for this reason than a fully grown human would be, so be especially careful if you encounter a mountain lion with you child or dog.

The best thing to do in the case of a mountain lion is to put your hands up like someone's pointing a gun at you, stare directly at it, and back away slowly and calmly until it is out of sight. If you have anything to make yourself bigger while you do this it can be helpful (E.g. I've taken my jacket off and held it between my arms in the "hands up, don't shoot" position to make it appear as if I were as tall as my outstretched arms).

If the mountain lion begins to act aggressively to you, you should now begin to make as much noise as possible and make it think you are more trouble than you are worth. If you can arm yourself, that's great, but try not to crouch or run to get a weapon. Do not try to run from it under any circumstances. They are faster than you and big cats usually go for the throat first. Throw things at it, make noise, get angry, but don't run. If it is undeterred by your noise/thrown objects and closes the gap and tries to attack you, you have no choice but to try to fight back. Mountain lions aren't brawlers so if you make the cat think theres a 10% chance making you its next meal could result in harm to it, it will give up on you. That's about it, really. At this point you have either gotten away, been eaten, or have a nice new pelt, but you've done all you can to maximize your chances of getting away without making any physical contact with the mountain lion. LMK if you have any other questions re: wildlife/outdoors safety