Abstract: Two fundamental finiteness conditions in group theory are the properties of being finitely generated and of finitely presented. More general finiteness conditions using geometric and homological properties of groups were introduced by C.T.C. Wall. Until recently, it was unknown whether the homological conditions implied the geometric conditions. M. Bestvina and N. Brady showed that this is not the case. They constructed counterexamples using right angled Artin groups and a piecewise linear version of the Morse theory. Purpose of this talk is to introduce these groups and see some applications.