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An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a reference text for the basic theory of Hopf algebras, in particular the Hopf algebras of symmetric, quasisymmetric and noncommutative symmetric functions and connections between them. The second goal is to give a survey of results with respect to an exciting new basis of the Hopf algebra of quasisymmetric functions, whose combinatorics is analogous to that of the renowned Schur functions.

Combinatorial analysis. --- Combinatorics. --- Quasisymmetric groups. --- Schur functions. --- Schur functions --- Quasisymmetric groups --- Combinatorial analysis --- Engineering & Applied Sciences --- Computer Science --- Hopf algebras. --- Combinatorics --- Algebras, Hopf --- S-functions --- Schur's functions --- Mathematics. --- Topological groups. --- Lie groups. --- Applied mathematics. --- Engineering mathematics. --- Algorithms. --- Topological Groups, Lie Groups. --- Applications of Mathematics. --- Algebra --- Mathematical analysis --- Algebraic topology --- Holomorphic functions --- Topological Groups. --- Math --- Science --- Groups, Topological --- Continuous groups --- Algorism --- Arithmetic --- Foundations --- Engineering --- Engineering analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Mathematics