0. Preface


This online Textbook based on half-year course APM441 at Department of Mathematics, University of Toronto but contains many additions.

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This Textbook is open (which means that anyone can use it without any permission or fees) and open-source (which means that anyone can easily modify it for his or her own needs) and it will remain this way forever. Source (in the form of Markdown) of each page could be downloaded: this page's URL is


and its source's URL is


and for all other pages respectively.

Victor Ivrii
Department of Mathematics
University of Toronto

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