The main objective of this work is to construct all the regular representations of the complex classical groups. Since each of these groups is reductive, in the sense that every regular module is a direct sum of irreducible regular modules, it su ces to construct the irreducible ones. We achieve this by using Weyl's method, which provides an explicit and concrete realization of each of the desired modules. Chapters 1 to 3 contain background information. The reader may choose to skip them and consult them only when necessary. Chapters 1 and 3 describe the relationship between the classical groups and their Lie algebras, with emphasis on the representation theory aspects of such objects. Chapter 2 summarizes many important results on the representation theory of complex semisimple Lie algebras. The actual work begins in Chapter 4, where we use Young diagrams and tableaux to construct all the irreducible complex representations of the symmetric groups. Surprisingly enough, these modules serve as building blocks to obtain all the desired representations of the complex classical groups, which is done in Chapters 5 through 7.