The main process to solve the problem of quantum and gravity is Mordern AG (global GLC) M→ Derived AG (local GLC) O-localizing Grothendleck's dream comes in Grothendeck's quantization of gravity Complete Einstein's dream UFT Analytic stack (analytic AG) The Langlands duality from the M-theory is a part of U-duality,the M- theory and its dynamics give us the global geometric Langlands corre- spondence [15] simplified by combining math and physics. D≤11-mod (Bung) ← → QCoh (LocSys)11 where Ğ is the Langlands dual group acting on the F-dual part of M-brane. Generally,construction of the M-theory is based on the modern alge- braic geometry with category theory.Studying the dynamics of the M- theory is based on that with higher category theory (representation of underlying space). The former gives an unification of superstring theories (Superstring theories type) → retract (Stype) Є Mpre Retracted from fibered category of superstring theories to stack of Lie groupoids. And the latter gives us a well defined stackified flow which is retracted from a non-solvable theory. Combing them, we successfully estab- lish an experiment-free theory with left evolution where M-flow~-flow, O-sense Fis the 2-nonexistence. In the end, derived algebraic geometry gives us further support to summarize all things and we find the M'-theory is the theory of everything originally proposed by Albert Einstein. Preview. A pre M-theory is a geometric stack written by Mpre = (ETSchSupGen (M), P(T), P, II) The M-theory M is a generalized super algebraic geometric stack Au= P(U)1: M→ Mprep V Mre cons. cons. We also put things into derived algebraic geometric n-stack and analytic derived stack to achieve our final goal completing TOE which is a category of no definition objects O-Sense~ Def 'UFT.