This book addresses the problem of teaching the Electronic Structure and Chemical Bonding of atoms and molecules to high school and university students. It presents the outcomes of thorough investigations of some teaching methods as well as an unconventional didactical approach which were developed during a seminar for further training organized by the University of Bordeaux I for teachers of the physical sciences. The text is the result of a collective effort by eleven scientists and teachers: physicists and chemists doing research at the university or at the CRNS, university professors, and science teachers at high-school or university level. While remaining wide open to the latest discoveries of science, the text also offers a large number of problems along with their solutions and is illustrated by several pedagogic suggestions. It is intended for the use of teachers and students of physics, chemistry, and of the physical sciences in general.