"Algorithmic Information Theory" is a textbook that deals with the processing of information, placing a particular emphasis on the algebraic aspects. It offers deeper insights into the algorithms that connect both polynomial and matrix algebra. The content is based on a series of lectures and has evolved over the years. The book is divided into five chapters, each addressing different topics in discrete mathematics with increasing levels of difficulty. The first two chapters are at an introductory level and cover data compression and cryptography, assuming a solid understanding of quotient rings and finite fields. Readers are guided through the complex landscapes of bit streams, gaining valuable insights into the underlying algorithms.