This book is intended for those who are interested in understanding the electronic structure and properties of polymers. The scope of the book is to provide the non-specialist reader with a comprehensive and unified description: (i) of quantum mechanical methods, mainly originating from quantum chemistry, to calculate the electronic properties of polymers, (ii) of their use for interpreting and predicting results in fields where the electronic structure is playing an important role, like the electrical conductivity and the non linear optical properties of conjugated polymers.It will also serve as a reference book to lecture graduate students on the electronic structure of polymers or more generally of quasi-one dimensional materials. In this framework, it is worth stressing that the quantum theory of polymers bridges the gap between chemistry and physics. Since no book of this kind involving a strong interaction between theoretical and experimental concepts is available at the moment, it will also meet a need for a timely monograph in a field of important and fast growing interest.