What Do I Do If I Encounter A Mountain Lion (cougar, Puma)?

Under no circumstances should you submit to your first impulse: run.
A running person will be perceived by the lion as prey, and your chances of being attacked will skyrocket. In California's first lion fatality in almost 100 years, a woman jogging alone in a remote area was killed and partially eaten.
Look the lion straight in the eye and back up slowly as you speak to it in a firm, loud voice. Make yourself look bigger by pulling your shirt or jacket up over arms held straight up over your head.
When a mountain biker in California realized he was being stalked by a lion, he stopped, raised his bike up over his head, and yelled at the animal. The bewildered cat bounded off.
If you are attacked, fight back vigorously, using an object or your arms and legs. A couple in their mid-70s was recently hiking in a park in the San Francisco Bay Area when a lion suddenly attacked the husband. The wife beat the cougar with a branch, and it abandoned the attack. Before she ran for help, she provided the victim with branches to defend himself the best he could if the cat returned.
The husband received serious lacerations to his head and one eye, but survived. Rescue personnel said he would have been killed had the wife not fought back.
Keep dogs restrained and quiet in lion country. Cougars have a natural antipathy to dogs, and you may be injured in the ensuing attack.
Make sure you keep close watch on young children. There have been several reports recently of toddlers being attacked on trails or in campgrounds.
A 20-year  moratorium on hunting lions has produced a population explosion of the big cats so encounters with humans are increasing.