This book presents a detailed analysis of the foundations of supermanifold theory. The approach followed, which is a modification of the DeWitt-Rogers approach, allows for a straightforward and consistent development of the basic geometry of these objects. The topics presented include: a general presentation of graded manifolds according to the Berezin-Leites-Kostant definition; a cursory exposition of Rogers' supermanifolds; basic definitions related to supermanifolds; Rothstein's axiomatics revisited; the cohomological properties of supermanifolds; bundle theory, including some elements of a theory of characteristic classes; the foundations of a theory of super Lie groups.
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