It could be the float in the tank is not working right. Try taking the ceramic lid off the tank and lifting up the arm that has a ball shaped float on the end of it, you should see this item right away when you look in the tank. There should be an adjustment screw or knob on the upright pole that the float is attached to; just turn it one way or the other to see if it makes a difference with water filling the tank--one way will allow more water to come in, the other will stop the water at a lower level.
While your'e there, make sure it is free of dirt by cleaning with an old toothbrush and water. Of course (like everything!) this whole mechanism could be broken which would require it to be replaced. Also there is a rubber flapper that closes the opening from the tank to the toilet itself; this may not be sealing correctly or the chain that lifts it up with each flush may be in the way of it closing properly. Adjust the chain if needed so it is able to close the hole, and or replace the flapper. I hope this can help you!
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