Algebra for Applications : Cryptography Secret Sharing Error Correcting Fingerprinting Compression This book examines the relationship between mathematics and data in the modern world. Indeed modern societies are awash with data which must be manipulated in many different ways: encrypted compressed shared between users in a prescribed manner protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory. This book provides the necessary background in arithmetic polynomials groups fields and elliptic curves that is sufficient to understand such real life applications as cryptography secret sharing error correcting fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third year undergraduates it is self contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self study