The articles in this exceptional book contain regular papers, extended papers and reviews, and thus vary in length and are useful for all kinds of audience. They describe, as the book's name suggests, HTSC models and methodologies. Physical models (like extended BCS model, bipolaron model, spin bag model, RVB (resonating valence bond) model, preformed Cooper pairs and antiferromagnetic spin fluctuation (AFSF) based models, stripe phase, paired cluster (spin glass (SG) frustration based) model, Kamimura-Suwa (Hund's coupling mechanism based) model, electron-plasmon interaction, electron- phonon interaction, etc.), theoretical methods (methodologies) (like generalised BCS-Migdal-Eliashberg theory, Hubbard model, t- J model, t- t'- U model, Hubbard-Holstein model, Fermi-, non Fermi- and marginal Fermi- liquid concepts, generalised Hartree-Fock formalism, etc.) and, experimental status and methodologies are all described there. For comparison with cuprates, fullerenes, ruthenates, organic-, non Cu-containing oxide-and conventional (elemental, A15)- superconductors, molecular crystals, nickelates, manganites, borides etc. are also discussed.