Construction of non-perturbative QFT and strings is the key to understand many outstanding problems in current physics. We propose to use A\_infinity structures to model spaces. It unifies spaces appeared in regularizations of QFT and in string field theories. There are natural effective theories over such spaces like matrix models. They are governed by gauge symmetries. Large N limit exists in some cases. It gives non-perturbative formulation of some QFT's and strings.