Physics 583 (QFT II) Spring 2021 Zoom lecture on Tuesday March 23, 2021. Today we covered renormalization of 𝜙^4 theory to two loop order by dimensional regularization with minimal subtraction and we used it to compute the two-loop beta function and the anomalous dimension. In the second half of the lecture we begin the discussion of the non-linear sigma model. We first introduced several generalizations (the CP^N-1 model, the principal chiral field and models on homogeneous spaces and their uses in string theory and Anderson localization).