The book starts with a history of Cryptography from antiquity to present day. It then continues with Public Key Cryptography, extensively treating the security of Advanced Encryption Standard (AES) at the state of the art level. An overview of main Public Key cryptosystems is given in Chapter 3. Among other covered topics are the Diffie-Hellman and ElGamal protocols and various digital signature algorithms. Chapter 4 treats the use of systems of polynomials both in cryptography and cryptanalysis. Some of the material is frequently cited original research. The book is meant as a textbook at undergraduate and graduate level and for independent study.