This book focuses on lattice-based cryptosystems, widely considered to be one of the most promising post-quantum cryptosystems and provides fundamental insights into how to construct provably secure cryptosystems from hard lattice problems. The concept of provable security is used to inform the choice of lattice tool for designing cryptosystems, including public-key encryption, identity-based encryption, attribute-based encryption, key change and digital signatures. Given its depth of coverage, the book especially appeals to graduate students and young researchers who plan to enter this research area.