Abstract: Grothendieck predicted that the cohomological Brauer group of a regular scheme X is insensitive to removing a closed subscheme Z of X of codimension>=2. By Gabber's several results, the conjecture was settled except for some cases that concern p-torsion Brauer classes in mixed characteristic (0,p). In 2018, Cesnavicius established the remaining cases by using  tilting equivalence for perfectoid rings. My talks are aimed at discussing the basics of the theory of perfectoid adic spaces in detail and explaining Cesnavicius's proof in a comprehensible way. The first several talks can be viewed as a mini-course on perfectoid spaces, with no more prerequisites than basic topology and commutative algebra.