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An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. This book introduces readers to the algebra of quasisymmetric functions and its fundamental theory. Results and relevant new contributions are included which pertains to the dynamic new basis of quasisymmetric Schur functions. A state-of-the-art summary is included with respect to an exciting new basis of algebra, which is the basis of quasisymmetric Schur functions, whose combinatorics is analogous to that of the renowned Schur functions.