This book brings a modern exposition of complex topological K-theory. It is designed for beginners in the field of K-theory, primarily for graduate students. The exposition is quite self-contained and the author has reduced the number of prerequisites for reading to a minimum. On the other hand, the text is not very long, consisting of only 208 pages. This was possible because the author has limited the exposition to the most central and classical part of K-theory, namely the above mentioned complex topological K-theory. No other parts of K-theory are included. Nevertheless, the reader can find here hints for reading about other parts of K-theory. Vector bundles are often studied here in terms of idempotents and invertible matrices over Banach algebras of continuous complex-valued functions. We should also remark that the last quarter of the book deals with characteristic classes of vector bundles in the Chern-Weil style. Each chapter is followed by exercises. Generally we can say that the presentation is very nice and the book can be strongly recommended.