An introduction to the statistical mechanic of classical and quantum spin systems. Phase transitions, critical phenomena, scaling limits, and quantum circuits and entanglement in extensive systems. The goal is to present the physic phenomena and principles in a manner enabling also rigorous results on the subject. The lectures start with a brisk review of what was covered in Fall 2024, and continue beyond that with a more extended, though still self contained, discussion of quantum spin array, and extended quantum circuits.