The article describes the methodology of the development of critical thinking of the individual in the conditions of the university. The essence, the hierarchy of the categories "criticism", "critical thinking" are analyzed from the philosophical, psychological and pedagogical points of view. The levels of development of critical thinking of future teachers (initial level, intermediate level, high level) are characterized.

The content of the methodology for the development of critical thinking of future teachers is offered on the model of the elective course program "Fundamentals of critical thinking" for students of 2-3 courses of higher education institutions. The content of the elective course, which we offer in the article, covers several topics. These are: "the content of normative legal acts related to the development of critical thinking of future teachers"; the philosophical Genesis of the concept of "critical thinking"; psychological and pedagogical features of the development of critical thinking; the main categories of the concept of critical thinking ("criticism", "thinking", etc.); the concept of D.D. Kluster's The methodological significance of the development of critical thinking of the individual; the principles of the development of critical thinking through reading and writing; critical thinking – a means of forming a methodological base; identification of critical thinking, special diagnostics". The methodology proposed in the article is intended for students and university teachers, including 15 hours of lectures, 30 hours of practical classes.