The objective of the present paper is to give a survey of recent progress on applications of the approaches of Ringel-Hall type algebras to quantum groups and cluster algebras via various forms of Greens formula. In this paper, three forms of Greens formula are highlighted, (1) the original form of Greens formula cite{Green}cite{RingelGreen}, (2) the degeneration form of Greens formula cite{DXX} and (3) the projective form of Greens formula cite{XX2007a} i.e. Green formula with a $bbc^{*}$-action.
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