The book entitled 'Dynamical System-A Short Course' contains eight chapters. This book is written for UG and PG students. Chapter 1 contains matrices and operators， subspaces， bases and dimension. determinants， trace and rank. direct sum decomposition. real eigen values. differential equations with real distinct eigen values. complex eigen values. Chapter 2 includes complex vector spaces. real operators with complex eigen values. application of complex linear algebra to differential equations. review of topology in Rn. new norms for old. exponential of operators. Chapter 3 contains homogeneous linear systems. a non homogeneous equation. higher order systems. the primary decomposition. the S+N decomposition. nilpotent canonical forms. Chapter 4 includes Jordan and real canonical forms. canonical forms and differential equations. higher order linear equations on function spaces. sinks and sources. hyperbolic flows. generic properties of operators. significance of Genericity.