\setcounter{section}{-1} \section{Foreword} These notes form a brief overview of basic topics in a usual introductory course of algebraic topology. They were prepared for my series of lectures at the Okayama University in 2002 and rewritten in 2013. They cannot substitute standard textbooks. The technical proofs of several important theorems are omitted and many other theorems are not proved in full generality. However, in all such cases I have tried to give references to well known textbooks the list of which you can find at the end. I would like to express my acknowledgements to my former student Richard Lastovecki whose comments helped me to correct and improve the text. The notes are available online in electronic form at \begin{center} \url{http://is.muni.cz/el/1431/jaro2013/M8130/um/39015882/} \end{center}