Abstarct: In this thesis we investigate the theory of quantum information systems in the descxription of electronic and nuclear structures. One of the applications of the concepts and techniques of information theory is in the atomic, molecular and nuclear structures which will be discussed in both relativistic (Dirac equation) and nonrelativistic (Schrödinger equation) cases here. Such a procedure, leads to the information entropy of representation of relativistic and nonrelativistic systems which is a complementary to energy representation arising from density functional and wavefunction theories. In this procedure, the information concepts plays the most crucial role. The content of the thesis are in summary as following. In first, having discussed the information concept, some information measurements including standard deviation, Shannon entropy and Fisher information, are introduced and their characteristics are analyzed. Also, these measurements are studied for the nonrelativistic hydrogen (Coulomb potential) and pseudoharmonic systems in three dimensions and the corresponding uncertainty principles are obtained. In the following, the same measurements are determined in Klein-Gordon equation and frxamework in Dirac relativistic frxamework. Furthermore, the information measurements are investigated for time-dependent harmonic oscillators (Log-periodic oscillators). In the end, the global information entropy properties are studied for single-fermion systems. Next, the information entropy for a nucleon in nucleus and a particle in a (pseudo) relativistic analytical model of hypernucleus will be discussed.