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This thesis deals with Abelian complexity of infinite words, i.e., function describing complexity of a given infinite word using sets of Parikh vectors of finite factors of the word. Some of already known results for words generated by primitive substitutions (including connection between Abelian complexity, balance function, discrepancy function and matrix of a primitive substitution) are summarized. Then an explicit formula for Abelian complexity of infinite words associated with quadraticdoi:10.5281/zenodo.2112128 fatcat:j4gxptknm5dkbg5d65ccjnvmfu