We systematize the theoretical approaches towards assessment of school textbooks, analyze the existing practice of textbook evaluation, and justify the need to formalize the assessment criteria in order to improve objectivity. We also suggest a system of diagnosable (measureable) criteria for textbook assessment. The criteria are ranged depending on their functional load. Level-one criteria are used to assess the scientific content of the basic texts (conformance to the educational standard and accuracy of scientific terms). At level two, we assess the extent to which methodology of a specific science affects the content of textbooks. At level three, there is textbook structure: the content of supplementary and explanatory texts, illustrative materials and navigation tools. Level four is where the guidance techniques used in a textbook are assessed. Finally, level five is assessment of relevant didactic and guidance materials. The paper contains advice to enhance the textbook evaluation procedure applied when developing the national list of textbooks recommended by the Ministry of Education and Science of the Russian Federation. The developed system of criteria may also be used to perform comparative analysis of textbooks on the same subject, where there is choice between textbooks. We use the proposed system to perform comparative analysis and assess the quality of six economics high school textbooks, as well as to develop recommendations for economics and social studies teachers to select textbooks from the national list.