Does Catholicism teach that there is a cyclic creation of the world? Many religions, like Hinduism teach that the world is in a cycle of creation: creation then preservation then destruction (fading, annihilation) of the world then creation of a new world, in a repeated cycles, and so on.

The mysticism of many religions adopt this view, i.e: creation of the world is eternal process, coming from no beginning and going to no end, in repeated cycles.

What is the opinion of Catholic Church regarding this matter?
None of the main parts of Christianity adhere to a cyclic view of creation. The Christian scriptures speak of the creation of the world (meaning the universe) by God "in the beginning" (meaning that nothing happened before that). Christians consider the creation was "Ex Nihilo" meaning that it was from nothing - there was no material from which the universe was made.

Likewise the scriptures speak of an end times of being with God which will last for ever. The "new world" will not be destroyed, not even for another creation.