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An interesting notion of cubic n- normed linear space is introduced as a generalization of fuzzy n- normed linear space and interval-valued fuzzy n- normed linear space. This book comprises of six chapters and deals thoroughly with the theory of cubic n- normed linear space, cubic quasi n- normed linear space and cubic semi n- metric space. Various interesting results on the union and intersection of cubic n- normed linear space and cubic semi n- metric space are also provided. Given two cubic quasi n- normed linear space their equivalent condition is established by means of definition and results. This book will be useful to the learners and researchers in this field.