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This special issue of the "Condensed Matter Physics" journal is dedicated to Professor Ihor Stasyuk, a prominent scientist and lecturer who celebrates his 80th birthday on September 23, 2018. The articles in this collections represent different fields of the quantum many-body physics and solid state theory, where Prof. I.V. Stasyuk made significant contributions and obtained remarkable results.Ihor Stasyuk started his research work during his student years, when, together with his supervisor Professor Abba Glauberman and V.V. Vladimirov, he developed a "new form of polar model" and introduced the "site elementary excitation" operators -predecessors of the well-known Hubbard operators. These results were acknowledged by N.N. Bogolyubov and published first in Doklady Akademii Nauk SSSR [Soviet Physics -Doklady] in 1959 and later summarized in his Ph.D. thesis "The Method of Site Elementary Excitations in the Theory of Nonmetallic Crystals", which was successfully defended in 1963. Subsequently, he became an assistant professor at the Department of Solid State Theory and later at the Department of Theoretical Physics of the Ivan Franko State University of Lviv. During his time at the university, he obtained significant results in the theory of exchange interactions and ferromagnetism in strongly correlated electron systems, including development of the operator perturbation theory for models with local electron correlations and of Wick's theorem and diagrammatic techniques for Hubbard operators. Simultaneously, he initiated studies on the model description of dynamic and thermodynamic properties of complex hydrogen-bonded ferroelectric compounds and on the microscopic theory of optical effects in dielectric crystals. In 1978, Ihor Stasyuk had to leave the Ivan Franko State University of Lviv and spent the next five years of his scientific activity connected with the Institute of Applied Problems of Mechanics and Mathematics of the Academy of Sciences of Ukraine, where he started working on electron-deformation effects in semiconductors and systems with narrow bands, as well as of crystals with a cooperative Jahn-Teller effect. At that time, he developed a unified microscopic theory of the optical effects induced by external fields in dielectric crystals, including electro-gyration and piezo-optic effect.