Chapter 2 provides a fairly comprehensive presentation of the theory of Boolean algebras, including proofs of Tarski’s Fixed Point Theorem for lattices and a detailed proof of Stone’s Representation Theorem. It begins with an in-depth explanation of the concept of a lattice and develops this concept in order to introduce the notion of a Boolean algebra as a type of lattice, thus emphasizing order as the essence of Boolean algebras. It shows how a lattice can be transformed into a Boolean algebra, how a Boolean algebra can be viewed as a Boolean ring, and thoroughly discusses the concepts of ideals, filters, and ultrafilters—necessary for the development of nonstandard analysis. The chapter concludes with the proof of Stone’s Representation Theorem.