The word which means an ancient temple in the shape of a pyramid built in stepped levels was a what

The correct term is Ziggurat. These were built in Mesopotamia. They served as a sort of social center. Atop most of them there would be a shrine. Priests would use the shrines. They could be easily guarded so that non priests couldn't enter. They also included courtyards, storage areas, bathrooms and living areas. They were usually in the center of a city. 

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