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The first textbook of mathematical analysis, which was based on the scientific heritage of Newton and Leibniz, was called Infinitesimal Analysis (L'Hopital, 1696). Throughout the 18th century, the actual "infinitesimals" were constantly and effectively used in research, but distrust of them gradually grew, which already in the 19th century, when the epsilon-delta technique was developed, led to their expulsion from mathematics.

The situation changed when, in 1961, Abraham Robinson published his book "Non-Standard Analysis", which gave a modern justification for the infinitesimal method; at the same time, new (for that time) model-theoretic concepts were actively used. The application of the appropriate approach implies a certain skill in the transition from reasoning in the framework of non-standard models to "metamathematical" reasoning, and vice versa. The purpose of this mini-course is to provide a brief introduction to non-standard Robinson analysis.