Hewitt pioneered the construction of the hyperreals by means of an ultrapower construction (Hewitt, 1948).
Hewitt wrote the 1975 English translation of A. A. Kirillov's 1972 Russian monographElements of the Theory of Representations (Элементы Теории Представлений), and co-authored Abstract Harmonic Analysis with Kenneth A. Ross (1st edn., 1st vol. in 1963; 1st edn., 2nd vol. in 1970), an extensive work in two volumes.
Hewitt, Edwin; Ross, Kenneth A. (1963), Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations., Die Grundlehren der mathematischen Wissenschaften, vol. 115, Berlin-Göttingen-Heidelberg: Springer-Verlag, MR0156915
Hewitt, Edwin; Stromberg, Karl (1965), Real and abstract analysis. A modern treatment of the theory of functions of a real variable, New York: Springer-Verlag, MR0188387
Hewitt, Edwin; Ross, Kenneth A. (1970), Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups., Die Grundlehren der mathematischen Wissenschaften, vol. 152, New York-Berlin: Springer-Verlag, MR0262773