Abstract: This paper is devoted to the description and analysis of the topology of nonlinear control systems. First of all, we define linearizable systems. Secondly, the basic concepts of Whitney topology are introduced, and used to describe the topology of the collection of nonlinear control systems. Under this topology we have shown that lineaizable set is a measure zero set unless m=1 and n=2 with m the input number and n the dimension of the state space. Thirdly, we discuss the problem of general feedback linearization. Necessary and sufficient conditions are given when n=m+1. Finally, we show that when n=m+1, all systems but a measure zero set are linearizable.