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The study of linear response properties of atomic systems has acquired considerable interest because of present day experiments, which opened up vast arena of observational research in atomic physics. Linear response properties like the excitation energies, oscillator strengths, atomic lifetimes, transition probabilities, quantum defects etc. of atomic systems and of highly charged ions have been reported for atoms and ions using time-independent and time dependent coupled Hartree-Fock approaches. Study of doubly excited state and two electron one photon transition also share a part. Many new transition properties and interesting behaviour of their structural properties have emerged from the investigation. The entire content of this book was submitted for obtaining Ph.D. degree of Dr. Tapas Kumar Ghosh from Jadavpur University, India.