This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory.Contents:Basic Theory of Multiple Zeta Values:The Time Before Multiple Zeta ValuesIntroduction to the Theory of Multiple Zeta ValuesThe Sum FormulaShuffle Relations among Multiple Zeta Values:Some Shuffle RelationsEuler Decomposition TheoremMultiple Zeta Values of Height TwoApplications of Shuffle Relations in Combinatorics:Generalizations of Pascal IdentityCombinatorial Identities of Convolution TypeVector Version of Some Combinatorial IdentitiesAppendices:Singular Modular Forms on the Exceptional DomainShuffle Product Formulas of Multiple Zeta ValuesThe Sum Formula and Their GeneralizationsReadership: Graduate students and researchers in number theory.