This book describes computational methods used in quantum dynamics with emphasis on small quantum systems. Computational physics is a fundamental physical discipline at the forefront of physical research. Thus it is an indisputable fact that computational physics form part of the essential landscape of physical science and education. In the present state of scientific knowledge the importance of quantum dynamics is commonplace. Computational quantum dynamics involves the use of computer calculations and simulations to solve quantum physical problems. Following a brief introduction to quantum dynamics the book revisits approximation techniques based on perturbational theory and variationalmethods. This discussion includes Hartree-Fock and density functional theory and quantum Monte Carlo methods. The next chapter presents the concepts of finite differences. Central in this chapter is the discretization in time and space. Later chapters concentrate on discrete variable techniques based on orthogonal polynomials, finite element and B-splinemethods for both time-independent and time-dependent problems and the combination of different computational techniques. The final chapter contains a list of useful sources for computational software and program codes. This book is primarily aimed at advanced students and graduates and researchers in theoretical and computational physics or chemistry and bridges the gap between quantum textbooks and computational research. Although not essential, the reader should have a basic background in quantum physics and some knowledge of numerical analysis would be helpful in reading this book.