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This paper describes some experiences in solving a difficult problem: organization of teaching General Measurement Theory in a situation where neither widely accepted opinion on its structure and contents nor authoritative textbooks and didactical materials exist. The contents of the discipline's theoretical part and exercises are given. The obligatory minimum of the theoretical part includes studying the initial mathematical concept like sets, binary relations, and mappings; formal logic and algebraic foundations of measurement as a cognitive process; features of measurement on quantitative and qualitative scales; formal models for measurands and procedures; and ways of mathematical description and estimation of measurement errors. Typical assignments are described. Features of the course instructional process organization are considered.