Abstract
CONTENTS Introduction Chapter I. Linear algebra in superspaces § 1. Linear superspaces § 2. Modules over superalgebras § 3. Matrix algebra § 4. Free modules § 5. Bilinear forms § 6. The supertrace § 7. The Berezinian (Berezin function) § 8. Tensor algebras § 9. Lie superalgebras and derivations of superalgebras Chapter II. Analysis in superspaces and superdomains § 1. Definition of superspaces and superdomains § 2. Vector fields and Taylor series § 3. The inverse function theorem and the implicit function theorem § 4. Integration in superdomains Chapter III. Supermanifolds § 1. Definition of a supermanifold § 2. Subsupermanifolds § 3. Families Notes References