Feedback invited: errors, obscurities, typos, "stupid questions" and all. Text key: "^" for superscript, "_" for subscript, "\" for boldface. First instalment is a skeletal summary introducing 1. Clifford Algebras ____________________ A (nondegenerate) Clifford algebra Cl(p,q) over some "scalar" field --- usually the real numbers \R, occasionally the complex numbers \C --- extends it to polynomials in a set of transcendental "generators" subject to the usual arithmetic laws of polynomial rings, except that: multiplication of generators is anti-commutative; and generators square to +1 (p of them) or to -1 (q of them). Scalars are embedded in the algebra in the natural fashion, as elements of grade 0 (constant polynomials) or -1 (zero); vectors of dimension p+q as elements of grade 1 (linear polynomials). A "versor" is any element which conjugates vectors to vectors: if F is linear, then so is G = A^+ F A. Here A^+ denotes "reversion" of A, which acts as an inverse to the extent that the "magnitude" ||A|| == A^+ A is scalar. For most purposes, nonzero scalar factors are irrelevant; zero magnitude on the other hand indicates a non-invertible projection. It's fortunate that the reversion is easily computed: if the terms of A are broken down into subsums <A>_k by grade (number of generators) A = <A>_0 + <A>_1 + <A>_2 + <A>_3 + <A>_4 + ... then A^+ == <A>_0 + <A>_1 - <A>_2 - <A>_3 + <A>_4 + ... Finally, A is invertible just when ||A|| is nonzero. WFL