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The book discusses both continuous and discrete systems in a systematic and sequential approaches for all aspects of nonlinear dynamics. The content structure is logical and its sequential orientation provides readers a global view of the field. The systematic mathematical approach is adopted with impressive number of examples worked out in detail including exercises. The unique and new features are the combination of mathematical theories and physical intuition in the topics on oscillations, bifurcations, Lie symmetry analysis of nonlinear systems and chaos. Conjugacy relation among maps and its properties are described with proofs. It contains thirteen chapters. This book may be chosen for courses in dynamical systems and chaos, nonlinear dynamics, etc. for advanced undergraduate and postgraduate students in Mathematics, Physics and Engineering Sciences. The mathematical foundation of chaos theory and its connection with fractals along with symmetries of nonlinear systems are the key points of this book.