The book entitled ‘Dynamical System – A Short Course’ contains eight chapters. This book 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. 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. homogeneous linear systems. a non homogeneous equation. higher order systems. the primary decomposition. the S+N decomposition. nilpotent canonical forms. 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. dynamical systems and vector fields. the fundamental theorem. existence and uniqueness. continuity of solutions in initial conditions. on extending solutions. global solutions. global solutions. the flow of a differential equation. nonlinear sinks. stability. Liapunov function. gradient systems.