Craftsman Eager-1 push mower is cranking, runs for a little then shuts off. What cause this? I have replaced the spark plug. Where do I go from there?

Several things can cause this and the first one to check is the fuel filter. It may be partially plugged and allows fuel to pass too slowly. Install a new filter or temporaily bypass it. Come back and tell us if things improved and we'll go from there

Check for contaminated fuel.

I'm going to guess that this is a Briggs engine on this. If so, there is a brass bolt on the bottom of the carb bowl. You need to unscrew this brass bolt, take it out. There will be tiny little holes in this bolt. You need to blow them out and make sure they are not obstructed, then put it back together and you should be good to go. Often, debris get the holes plugged up. The engine will start and die quickly after.
Hope this helps and may God bless,
Pete

I just replaced the carburetor, spark club, and air filter. The mower still quit after a few minutes of running. As it turns out, it was a faulty gas cap that was not venting properly. The faulty gas cap caused a vapor lock, not allowing fuel to flow to the engine. While the engine is sputtering, loosen the gas cap and see if the engine recovers from sputtering. If so, replace the gas cap and the problem will be fixed.