The conclusive volume of the Brandeis University Summer Institute lecture series of 1970 on theories of interacting elementary particles consisting of five sets of lectures. The five sets of lectures are as follows: Rudolph Haag (II. Institut fur Theoretische Physik der Universitat Hamburg) on "Observables and Fields": introduction; axiomatic quantum field theory in various formulations; structure of superselection rules; charge quantum numbers; statistics; parastatistics. Maurice Jacob (CERN, European Organization for Nuclear Research) on "Regge Models and Duality": introduction; duality in a semi-local way; duality and unitary symmetry; dual models for meson-meson scattering; dual models for production process; from dual models to a dual theory. Henry Primakoff (University of Pennsylvania) on "Weak Interactions": introduction; lepton conversation and the implications of a possible lepton non-conversation; first-order and second-order weak collision processes; "abnormalities in the weak currents and how to discover them; conclusion. Michael C. Reed (Princeton University) on "The GNS Construction—A Pedagogical Example": infinite tensor products of Hilbert spaces; the canonical anti-commutation relations; the example; the example—via the GNS construction. Bruno Zumino (CERN, European Organization for Nuclear Research) on "Effective Lagrangians and Broken Symmetries": Introduction; effective action and phenomenological fields; Ward identities and the effective action; Goldstone's theorem; non-linear realizations; massive Yang-Mills fields as phenomenological fields; broken scale invariance; the fifteen parameter conformal group and the Weyl transformations; conversion identities and trace identities; invariant actions; SU(3)xSU(3) and conformal invariance; strong gravitation; concluding remarks.