Abstract: Since tropical geometry, the main topics of this talk belong to, is an algebraic geometry over a semifield called tropical semifield, we first explain classical algebraic geometry, in particular, the duality of geometry and algebra. Next, we give a brief introduction to tropical geometry. This includes its history, sources, easy examples and important theorems. Then focusing on the tropical version of duality of geometry and algebra, we explain how tropical rational function semifields are well-behaved, i.e., my results on them.