After a short and slightly provocative “computational” introduction to
Clifford algebras, two problems will be discussed in the seminar. In the first, 
we shortly present how two-level model in physics can be reformulated and solved 
in a purely geometric way by Clifford algebra. In the second, a detailed introduction 
into problem of inverse of multivector when n=p+q<7 will be presented. It is hard to 
believe that after seminal work published 130 years ago (in 1878) by Clifford, one 
of the fundamental problems — the inverse of a general multivector — still has no answer. 
Finally, if time will allow, an example on how the noncommutative multivector
Clifford-Sylvester equation  (AX+BX=C, p+q <= 3) can be solved by inverse multivector
algorithm will be demonstrated.