The first volume of the Brandeis University Summer Institute lecture series of 1970 on theories of interacting elementary particles, consisting of four sets of lectures. Every summer since 1959 Brandeis University has conducted a lecture series centered on various areas of theoretical physics. The areas are sufficiently broad to interest a large number of physicists and the lecturers are among the original explorers of these areas. The 1970 lectures, presented in two volumes, are on theories of interacting elementary particles. The four lecturers of Volume 1, and the range of the topics they cover, are as follows: Stephen L. Adler (Institute for Advanced Study) on "Perturbation Theory Anomalies": introduction and review of perturbation theory; the VVA triangle anomaly; absence of radiative corrections; generalizations of our results; connection between Ward identity anomalies and commutator (Bjorken-limit) anomalies; applications of the Bjorken limit; and breakdown of the Bjorken limit in perturbation theory. Stanley Mandelstam (University of California at Berkeley) on "Dynamical Applications of the Veneziano formula for the four-point scalar amplitude; factorization; the operator formalism; Veneziano-type quark models; and higher-order Feynman-like diagrams. Steven Weinberg (Massachusetts Institute of Technology) on "Dynamic and Algebraic Symmetries": Introduction; hadron electrodynamics; local symmetries; and chirality. Wolfhart Zimmermann (New York University) on "Local Operator Products and Renormalization in Quantum Field Theory": introduction; renormalization; operator product expansions; and local field equations. The second volume contains lectures by Rudolf Haag on observables and fields, by Maurice Jacob on duality, by Michael Reed on non-Fock representations, and by Bruno Zumino on effective Lagrangians and broken symmetries.