The course is dedicated to PhD students. Lectures introduce participants to basics and modern concepts in the solid state physics, such us: the first and the second quantization language for single and many-particle systems, fermions, bosons and quasiparticles, tight-binding methods, phonons, electron-phon coupling,
quantum Hall effect, graphene, silicene nanostrutures, Dirac and Majorana fermions, BCS theory, p,d-wave superconductors, topological insulators and superconductors, QFT, Fermi surfaces, XPS, ARPES, SvH effect, transport through quauntum dot in weak and strong coupling regime, Kondo effect, merons, band structure, equation of motion and time-dependent Green's functions. The lectures include exercises and examples with using two freeware Mathematica packages : Sneg and GTPack.