The molecular orbital (MO) and valence bond (VB) theories of the electronic structure of molecules emerge from one quite general approximation method involving the use of anti-symmetrized products (AP's) of one-electron wave function ('orbitals'), differing fundamentally only in their choice of a first approximation; in MO theory this is usually a single AP, and the orbitals are non-localized molecular orbitals, but in VB theory it is always a combination of many AP's, the orbitals being localized atomic orbitals. The MO theory lends itself well to rigorous formal development and has recently been employed in essentially ab initio calculations; but a corresponding development of the existing VB method is precluded by the technical necessity of neglecting large numbers of non-vanishing integrals. The present papers are devoted to a reformulation of the VB method in which the usual difficulties are circumvented; the revised method is no less powerful than an MO approach in which full configuration interaction (i.e. refinement of the wave function by addition of 'excited state' AP's) is admitted. The first paper is essentially preparatory. Orbital theories involving many AP's are discussed generally but with emphasis on the origin and concepts of the VB approach. Analysis of the charge distribution in a molecule is then shown to provide a unified description of chemical bonding and a general method of defining a 'bond order', applicable in any orbital theory. Against this background the existing VB theory is critically discussed. The validity of the whole approach rests upon the assumption of approximate orthogonality of the basic orbitals; an attractive method of making the theory rigorous, whilst retaining its formal structure, would therefore involve the use of accurately orthogonal basic orbitals. But a treatment of the hydrogen molecule along such lines leads to an apparent paradox; the formally 'covalent' VB structure describes only strong repulsion between the 'bonded' atoms. This paradox is resolved and certain general characteristics of the revised VB theory are tentatively inferred.