The article aims to consolidate the topogical foundation needed for Faltings' approach in p-adic Hodge theory. Topics discussed include the two steps of Faltings' approach such as the generalization of the Galois techniques and the p-adic étale cohomology of schemes over p-adic local fields, the covanishing topology of Deligne, and correcting the definition of the topologies introduced by Faltings.