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The problem about invertibility of Keller maps is Jacobian Conjecture(JC for short).The JC is raised by Keller in 1939.This conjecture give an equivalent statement about the invertibility of a Keller map.In addition,to study the structure of polynomial automorphisms is another important topic,which is closed connected with JC.The linearly dependent problem and the linearly triangularizability of Keller maps are raised in the process of studying JC and the structure of polynomial automorphisms.We first discuss the JC for some special polynomials and the degree of the inverse of polynomial automorphisms.Then we give an equivalent problem of the JC and discuss when the problem has an affirmative answer.Finally,we discuss the linear triangularizability and the irreducibility of some Keller maps and give a negative answer to the structural conjecture.