Abstract: Following an idea of Mitchell, a k-algebra, A, can be thought of as a k- category with a single object. Therefore, it is natural to ask how properties of A can be generalised to the "many objects case". Happel in his paper "On Gorenstein algebras" proved many interesting results on Iwanaga-Gorenstein algebras. The aim of this talk is generalise these results to the many objects case, that is to define and study Iwanaga Gorenstein k-categories.