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1 Dynamical Systems-An Introduction 1.1 Dynamical systems 1.2 Continuous dynamical systems 1.3 Discrete dynamical systems 1.3.1 Discrete logistic model 1.3.2 The tent map 1.4 Topological dynamical systems 1.5 Chaos and chaotic dynamics. 1.5.1 General discussion 1.5.2 Cantor set. 1.5.3 Chaotic maps in the interval 1.5.4 Set-valued chaos 1.5.5 Uniform convergence and chaotic behavior 1.5.6 Bifurcation in one-dimension 1.5.7 Stability 1.6 Sharkouskii's Theorem 1.7 Symbolic dynamical systems 1.8 Topological entropy 1.9 Schwarzian derivative 1.10 Applications of chaos 1.11 Organization of the book 1.12 Exercises . 2 Sequence of Maps and Chaos 2.1 Prelude 2.2 Mathematical preliminaries 2.3 Sequence of maps in the successive way 2.4 Sequence of maps in the iterative way 2.5 Few examples. 3 Some Features of the Generalized Shift Map 3.1 Prelude 3.2 Mathematical preliminaries 3.3 Chaoticity of the generalized shift map 3.4 Some stronger chaotic properties of the generalized shift map 3.5 Some special properties 3.6 Conclusions 4 Dynamics of the Uniform Limit of Sequence of Maps 4.1 Prelude 4.2 Mathematical preliminaries 4.3 Chaotic behavior of the uniform limit function 4.4 Conclusions 5 Sharkovskii's Theorem 5.1 Prelude 5.2 Mathematical preliminaries 5.3 Main theorems 5.4 Further discussions on Sharkovski's Theorem 6 A New Model of Chaotic Dynamics 6.1 Prelude 6.2 Mathematical preliminaries 6.3 Main theorems 6.4 Some special properties