Craftman lawnmower start and turn off and do not stay running .

Sounds like you have an issue with carb main jet. Latter needs cleaning or carb rebuild or replacement.

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Start by adjusting your carb 1 full turn out on the low and high side. This should start and let it run. Then if it bogs down while accelerating, turn the low side out another quarter to half turn. You could also have fuel line, fuel filter or other fuel issues.

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Check oil breather for being plug-up.

Go to www.managemylife.com and get a manual.

Clean and rebuild your carb, your problem lies in the carb.

The charging system is under the flywheel, but first check the 2 wires are connected at the side of the motor, they might be black and white at the conector.

The ignition module on the engine may have gone bad. it may need to be replaced. Plus check air filter to make sure it is clean.

First,make sure you are sitting in the seat as the seat has a safety switch under it that will prevent it from starting if noone is on it.
Check for spark,If no spark,Coil is not working.
Check for fuel at carb,If no fuel,check filter and Carb may needs cleaning or replaced.

If you have spark and fuel and it still won't start,It is a timing issue.