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In this review paper, we illustrate a possible route to obtain a reliablesolution of the 2D Hubbard model and an explanation for some of theunconventional behaviours of underdoped high-$T_\text{c}$ cupratesuperconductors within the framework of the composite operator method. Thelatter is described exhaustively in its fundamental philosophy, variousingredients and robust machinery to clarify the reasons behind its successfulapplications to many diverse strongly correlated systems, controversialphenomenologies and puzzling materials.

The composite operator method route to the 2D Hubbard model and the cuprates