Scope and Method of Study: The purpose of this research was to experimentally study quantum dynamics of systems whose classical dynamics are chaotic. Quantum delta-kicked systems such as kicked rotor and kicked accelerator were used. The cold non condensed atoms were kicked first to realize the kicked accelerator. Among the objectives were the realization of resonances of the kicked accelerator and associated phenomena of quantum accelerator modes using a Bose-Einstein Condensation (BEC). One of the major achievements of the work in this thesis was the creation of the quantum delta-kicked rotor and its associated resonances to realize a quantum ratchet. The properties of the ratchet were studied in detail.