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These notes provide an explanation of the type classification of von Neumannalgebras, which has made many appearances in recent work on entanglement inquantum field theory and quantum gravity. The goal is to bridge a gap in theliterature between resources that are too technical for the non-expert reader,and resources that seek to explain the broad intuition of the theory withoutgiving precise definitions. Reading these notes will provide you with: (i) anargument for why "factors" are the fundamental von Neumann algebras that oneneeds to study; (ii) an intuitive explanation of the type classification offactors in terms of renormalization schemes that turn unnormalizable positiveoperators into "effective density matrices;" (iii) a mathematical explanationof the different types of renormalization schemes in terms of the allowedtraces on a factor; (iv) an intuitive characterization of type I and II factorsin terms of their "standard forms;" and (v) a list of some interestingconnections between type classification and modular theory, including theargument for why type III$_1$ factors are believed to be the relevant ones inquantum field theory. None of the material is new, but the pedagogy isdifferent from other sources I have read; it is most similar in spirit to therecent work on gravity and the crossed product by Chandrasekaran, Longo,Penington, and Witten.

Notes on the type classification of von Neumann algebras