This textbook on  Theoretical Foundations of Computer Science has been largely inspired by the style of teaching practiced by Vladimir Lifschitz during my years at the University of Theoretical Foundations of Computer Science Texas at Austin. It was Spring 1999 when I took CS 336 titled "Analysis of Programs" and devoted to proofs of program correctness. Vladimir Lifschitz class surveyed mathematical techniques useful in the analysis and verification of programs. In his teaching, Dr. Lifschitz relied on a set of concise lecture notes consisting of mathematical definitions and problem statements. The students were tasked to study the definitions, and use these to tackle the given problems at home. Then, a lecture hall would turn into an interactive classroom, where students would present their solutions on a blackboard. This style of teaching mathematics is attributed to Robert Lee Moore, a topologist who practiced this art at the University of Pennsylvania when he began teaching  in 1911.

This textbook is meant to assist the instructors in introducing elements of Moore's style of teaching into their classroom. It can also be used in a more traditional settings, where the content of the textbook serves the basis for classical lectures while the students can be tasked from time to time with the exercises sprinkled across the text. As a textbook it not only lists the definitions but also illustrates these on examples and provides solutions to some of the stated problems. This text attempts to present material as concisely as possible. In addition, sections contain exercises. These are meant to be solved by students. The content of the book should be all that the students need to tackle these problems. As such the text can be used for the self study of the material. The conciseness of the text should not allude that the material presented is of great simplicity, rather the students are invited to experience the beauty and complexity of the material by putting their thoughts and effort into solving exercises.