This chapter sets out some of the fundamentals of modern chemistry. It chronicles the historical development of our current understanding of the structure of the atom – at least as far as is necessary from a chemistry perspective. (For more information on the history of chemistry, see Partington [1961–70] and Hudson [1992].) The work summarized here was so important that it was honored by the award of numerous Nobel Prizes to some of the most famous chemists. We follow the development of our understanding through the identification of the nature of the proton and electron, and subsequently the neutron. Following a review of the discovery of the various particles emitted during natural radioactivity, we present the basic model of the nuclear atom surrounded by orbital electrons. This model allows us to understand radioactive stability and the existence of isotopes. We then venture into the exotic world of quantum chemistry, in order to explain the stability of the orbital electrons, and the concept of atomic energy levels. (For an introduction to the development of quantum theory see McEvoy and Zarate 1999.) This introduces the concept of quantum numbers, which then leads to a set of simple rules to understand the way in which electron orbitals are filled as the size of the atom increases. This in turn leads to an understanding of the construction of the modern periodic table, which is the key to understanding the chemical behavior of the inorganic elements and compounds.