Short answers, pulled from the story.
A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. It may result from the electrostatic force between oppositely charged ions, the sharing of electrons, or a combination of these effects, and it determines the structure and properties of matter.
The main strong bonds are covalent, ionic, and metallic, while the weak secondary bonds include dipole-dipole interactions, the London dispersion force, and hydrogen bonds. In a covalent bond electrons are shared, in an ionic bond an electron is transferred, and in metallic bonding electrons are donated to a shared sea between many atoms.
In a covalent bond two or more atoms share valence electrons more or less equally, while in an ionic bond an electron is transferred, leaving one atom positively charged and the other negative. An electronegativity difference above 1.7 is likely ionic, and a difference below 1.7 is likely covalent.
In metallic bonding each atom donates one or more electrons to a sea of delocalized electrons that move freely between many atoms. This free movement produces metals' electrical and thermal conductivity, malleability, high tensile strength, and the shiny lustre that reflects most frequencies of white light.
In 1916 the chemist Gilbert N. Lewis developed the concept of electron-pair bonds, in which two atoms may share one to six electrons to form a single bond, double bond, or triple bond. He wrote that an electron may form part of the shell of two different atoms and cannot be said to belong to either one exclusively.
In 1927 Øyvind Burrau derived the first complete quantum description of a simple bond in the hydrogen molecular ion H2+, and the same year Walter Heitler and Fritz London introduced the basis of valence bond theory. In 1933 H. H. James and A. S. Coolidge calculated the dihydrogen molecule's dissociation energy in close agreement with experiment, convincing scientists that quantum theory matched reality.