The review is devoted to the presentation of various mathematical descriptions of spacetime. This are the Minkowski spacetime, intuitionistical spacetime, non-commutative spacetime. The meaning of the idea of the non-fundamental concept of spacetime about which in the literature one speak as on the emerging spacetime is discussed. The spacetime of loop quantum gravity is demonstrated. The mechanism of the emergence of gravity and spacetime within AdS/CFT is given. It is shown as connectivity of spacetime is determined by the entanglement measure of quantum subsystems.