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The monograph consists of 3 articles. In the monograph, boundary value problems for second order and higher order quasi-linear parabolic equations are studied in appropriate Sobolev spaces. The monograph has been prepared at the Department of Mechanics and Mathematics, Western Caspian University. I express my gratitude to corresponding member of ANAS, Bilal Bilalov and professor Farman Mammadov for their special advice in the preparation of the monograph.