This text outlines the basic facts concerning Kekulé structures in benzenoid hydrocarbons: their history, applications and especially enumeration. The book is primarily aimed at organic and theoretical chemists interested in the enumeration of Kekulé structures of conjugated hydrocarbons as well as to scientists working in the field of mathematical and computational chemistry. The level of mathematics required from the reader matches the skills of normally educated undergraduate chemistry students. Furthermore, all important combinatorial formulas are exemplified and illustrated by pertinent special cases. The book may be of some relevance also to mathematicians wishing to learn about contemporary applications of combinatorics, graph theory and other branches of discrete mathematics.