This booklet concisely provides the newest tendencies within the physics of superconductivity and superfluidity and magnetism in novel platforms, in addition to the matter of BCS-BEC crossover in ultracold quantum gases and high-Tc superconductors. It additional illuminates the in depth alternate of rules among those heavily comparable fields of condensed subject physics over the past 30 years in their dynamic improvement. The content material relies at the author’s unique findings received on the Kapitza Institute, in addition to complicated lecture classes he held on the Moscow Engineering actual Institute, Amsterdam collage, Loughborough collage and LPTMS Orsay among 1994 and 2011. as well as the findings of his workforce, the writer discusses the newest ideas in those fields, got either in Russia and within the West. The publication contains sixteen chapters that are divided into 4 components. the 1st half describes fresh advancements in superfluid hydrodynamics of quantum fluids and solids, together with the modern topic of attainable supersolidity in quantum crystals of 4He, whereas the second one describes BCS-BEC crossover in quantum Fermi-Bose gases and combos, in addition to within the underdoped states of cuprates. The 3rd half is dedicated to non-phonon mechanisms of superconductivity in unconventional (anomalous) superconductors, together with a few very important elements of the idea of high-Tc superconductivity. |The final half considers the anomalous general kingdom of novel superconductive fabrics and fabrics with sizeable magnetoresistance (CMR). The booklet deals a invaluable advisor for senior-level undergraduate scholars and graduate scholars, postdoctoral and different researchers focusing on solid-state and low-temperature physics.