This thesis explores how partitions and partition lattices can provide insight into small-scale and large-scale analytical relationships in several twelve-tone compositions by Milton Babbitt. Chapter 1 outlines the concept of partition lattices, as they have recently been described by Richard Kurth; summarizes the definitions and conventions of the lattice model; and suggests how they might be applied to Babbitt's music. Chapter 2 examines how recurring hexachords and hexachordal partitions arise from lattice interactions of the trichordal array partitions in the Woodwind Quartet (1953). Chapter 3 applies the lattice model to the first twelve measures of the Composition for Viola and Piano (1950) and explores how partitions corresponding to the surface texture are all subpartitions of a single hexachordal partition. Chapter 4 examines how partition lattices suggest various different levels of partition structure in the String Quartet No. 2 (1954). Chapter 5 summarizes the conclusions of the preceding chapters, outlines the limitations of the analytical method, and discusses the possibilities for applying partition lattices to the all-partition array works of Milton Babbitt.