  We reorganize, simplify and expand the theory of contractions or interior
products of multivectors, and related topics like Hodge star duality. Many
results are generalized and new ones are given, like: geometric
characterizations of blade contractions and regressive products, higher-order
graded Leibniz rules, determinant formulas, improved complex star operators,
etc. Different contractions and conventions found in the literature are
discussed and compared, in special those of Clifford Geometric Algebra.
Applications of the theory are developed in a follow-up paper.
