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Scope/Content: Hugh Everett's long thesis was submitted to John Archibald Wheeler, his doctoral thesis advisor, in January 1956 under the title "Quantum Mechanics by the Method of the Universal Wave Function.'' It was retitled "Wave Mechanics Without Probability'' and circulated in April of that year to several prominent physicists, including Niels Bohr. Largely due to the criticism of the long thesis by the Copenhagen colleagues, Everett and his advisor John Wheeler rewrote Everett's thesis in the winter of 1957 to produce a much shorter version, which Everett subsequently defended for his Ph.D. under the title "On the Foundations of Quantum Mechanics.'' While the long thesis was organized around the quantum measurement problem and how it is best solved by pure wave mechanics, the short thesis presented Everett's relative-state formulation of pure wave mechanics more as a suitable theory for the development of quantum gravity, cosmology, and field theory. The short thesis no longer contains Everett's chapter on information theory and correlation, his survey of possible solutions to the measurement problem, or his extended discussion of the nature of physical theories. What remains is a distilled presentation of pure wave mechanics, his principle of the fundamental relativity of states, and his derivation of the standard quantum statistics. The short thesis was retitled for publication in Reviews of Modern Physics in July 1957 as "The `Relative State' Formulation of Quantum Mechanics.'' The version below closely follows the Reviews of Modern Physics article. The long thesis itself was not published until 1973 in the DeWitt and Graham Princeton University Press anthology. It was published under the title "The Theory of the Universal Wave Function." This document is a reproduction of the version of the thesis published in the DeWitt-Graham anthology. Scope/Content: This document is a reproduction of a paper appearing in "The Many World Interpretation of Quantum Mechanics," N. Graham and B. DeWitt eds., Princeton University Press: Princeton, 1973.