Advice re: lawn mower problem?

Hello:

Last year I bought what I though was a good mower (poulan with a briggs stratton engine). It has been used around 15 times and well taken care of. However this year I am having two recurring problems with it. First, 50% or more of the time it will not start. I check the gas, oil, spark plug, prime it, etc. Sometime I think I have the problem figured out (e.g., once the spark plug was wet so I dried it) but it goes back to not starting. Any thoughts on why this might be/most common causes of this?

Then last week it also started shutting itself off while I was using it. In a one hour cutting session (it was difficult to start at beginning) it shut off twice (and yes, lots of gas and oil)

Any suggestions for do it myself checks or fixes would be appreciated

Thanks