Among the many existing notions of higher categories, the notion of strict globular n-category is, in some sense, the most basic one. In this chapter, the essential definitions and notations are set. Starting with a description of the basic "shapes", that is, the presheaf category of globular sets, family of operations endowing a globular set with a structure of ω-category is defined. Then, it is proven that the category of strict ω-categories is exactly the category of algebras of the monad induced by the forgetful functor from ω-categories to globular sets. Finally, important subcategories of ω-categories, obtained by requiring cells to be invertible above a given dimension, are defined.