As this little book was primarily designed for the use of chemists and other non-mathematical readers I have added a section on diatomic molecules and above all much extended the chapters on the chemical bond. These are in the same elementary style as the rest of the book. I hope that these additions (which seem compatible with the idea of a small pocket book) will afford a good illustration of the methods of wave mechanics as well as its usefulness for chemical problems. To make the general theory more complete a section on the time-dependent wave equation has also been added.