  The topic of the review is the application of new ideas of unconventional
quantum states to the physics of condensed matter, in particular of solid
state, in the context of modern field theory. A comparison is made with
classical papers on many-electron theory, including the formalism of
many-electron operators. The essentially many-particle nature of the ground
state, individual and collective excitations, and quantum fluctuations in the
systems under consideration, as well as quantum phase transitions are discussed
with an emphasis on topological aspects and with allowance for the effects of
frustration. Variational approaches and representations of auxiliary particles,
corresponding mean-field approximation and gauge field theory,
confinement-deconfinement problem, violation of the Fermi-liquid picture, and
exotic non-Fermi-liquid states are considered. An overview is given of the
modern theory of entangled topological states, formation of spin liquid,
strings and string networks.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Soft Condensed Matter