This is the second edition of this textbook, the original of which was published in 2007. Initial undergraduate studies in physics are usually in an organized format devoted to elementary aspects, which is then followed by advanced programmes in specialized fields. A difficult task is to provide a formative introduction in the early period, suitable as a base for courses more complex, thus bridging the wide gap between elementary physics and topics pertaining to research activities. This textbook remains an endeavour toward that goal, and is based on a mixture of simplified institutional theory and solved problems. In this way, the hope is to provide physical insight, basic knowledge and motivation, without impeding advanced learning. The choice has been to limit the focus to key concepts and to those aspects most typical of atoms, molecules and compounds, by looking at the basic, structural components, without paying detailed attention to the properties possessed by them. Problems are intertwined with formal presentations of the arguments presented, designed as an intrinsic part of the pathway by which the student should move in order to grasp the key concepts. The text has been completely revised. The subject index has been considerably extended and some figures amended in order to help the reader to better perceive the physical issues. However, the general purpose of this text remains the same as in the first edition.