Abstract: We start with few historical notes concerning the birth of quantum chaos. Particular attention will be paid to the definitions of quantum chaos in view of its relation to classical chaos. Then, we discuss essential properties of quantum chaos in terms of both the energy/quasienergy spectra and eigenstates. Special interest will be devoted to such important quantities as local density of states (or, the same, strength function) and chaotic structure of eigenstates, as well as to the notion of quantum ergodicity and energy shell. The main attention will be paid to the onset of statistical description of quantum models, especially, to the problem of emergence of thermalization in closed many-body systems. Many other questions will be discussed, initiated by the audience.