In this paper, we present a detailed tutorial on linear cryp tanalysis and differential cryptanalysis, the two most significant attacks a pplicable to symmetric-key block ciphers. The intent of the paper is to present a lucid explanat ion of the attacks, detailing the practical application of the attacks to a cipher i n a simple, conceptually revealing manner for the novice cryptanalyst. The tutorial is base d on the analysis of a simple, yet realistically structured, basic Substitution-Permuta tion Network cipher. Understanding the attacks as they apply to this structure is use ful, as the Rijndael cipher, recently selected for the Advanced Encryption Standard (AES), has bee n derived from the basic SPN architecture. As well, experimental data from t he a tacks is presented as confirmation of the applicability of the concepts as outlined.