An Introduction to Algebraic Geometry and Algebraic Groups

This is a textbook on algebraic geometry with an orientation towards algebraic groups. The first two chapters may serve very well as a first course on algebraic geometry. Exposition is very clear and it proceeds relatively quickly. Starting from the third chapter, the text is devoted to algebraic groups. The main aim is to describe properties of algebraic groups of the Lie type over fields of positive characteristic. The author describes the structural theory of these groups, and in the fourth chapter, he takes into account the Frobenius maps. This leads in a natural way to finite groups of the Lie type. The whole book is a nice and relatively short text also presenting many interesting examples. Each chapter is completed by bibliographical remarks and exercises. The author’s intention was to write a quick introduction to the area of algebraic groups of the Lie type over fields of positive characteristic and I think that he was very successful. The first part of the book can be recommended as a very suitable text for undergraduate students, while the second part can be used by postgraduate students at the beginning of their studies. Finally, I agree completely with the author who can imagine it being suitable for someone who just wishes to study some basic aspects of this beautiful area of mathematics. I can only repeat that this area is very nicely presented in the book.

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