In the present paper we introduce and study the topological entropy of non-autonomous dynamical systems and define the non-autonomous dynamical system on Lie groups and manifolds. Our main purpose is to estimate the topological entropy of the non-autonomous dynamical system on Lie groups. We show that the topological entropy of the non-autonomous dynamical system on Lie groups and induced Lie algebra are equal under topological conjugacy, and a method to estimate the topological entropy of non-autonomous systems on Lie groups is given. To illustrate our results, some examples are presented. Finally some discussions and comments about positive entropy on nil-manifold Lie groups for non-autonomous systems are presented.

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