In this book, Professor Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography. The presentation is essentially self-contained with detailed proofs of all statements provided, yet without sacrificing readability. Professor Salomaa is well known for his books in this area; the present work will be welcomed as an exposition that begins with basics familiar to advanced undergraduate students yet proceeds to some of the most important recent developments in theoretical computer science.