[Part I, cf. Fundam. Theor. Phys. 94, 259-266 (1998; Zbl 0898.15028).]
One of the fundamental laws of population genetics is the Hardy-Weinberg principle. This can be formulated in mathematical terms as a Hardy-Weinberg quadratic form. Since Clifford algebras are the natural associative, unital algebras of a pair \((V,Q)\), \(V\) a linear space, \(Q\) a quadratic form, it is obvious to employ these algebras in mathematical genetics. The paper starts with a detailed description of weighted algebras suited for mathematical genetics and capable of modelling the Hardy-Weinberg principle in form of a Hardy-Weinberg quadratic form. A characteristic feature of such a principle is a special measure \(\omega\) which induces a real and imaginary part in the relevant algebras. A classification of genetic algebras and a study of their properties is most easily put forward in Clifford algebraic terms. Diploid and tetraploid populations with two alleles are studied. The biological interpretation of the mathematical outcomes of the Hardy-Weinberg laws remain to be discussed.