ABSTRACT
This chapter provides a detailed exposition of the first section of the famous paper Factoring polynomials with rational coefficients [88] by A. K. Lenstra, H. W. Lenstra Jr. and L. Lova´sz. This paper introduced the most important algorithm for lattice basis reduction. This algorithm is called the LLL algorithm after the initials of its authors. For a historical paper on the origins of the LLL algorithm, see Smeets [132].
