  This chapter gives an introduction to qualitative and quantitative
topological analyses of molecular electronic transitions. Among the
possibilities for qualitatively describing how the electronic structure of a
molecule is reorganized upon light-absorption, we chose to detail two of them,
namely the detachment/attachment density matrix analysis and the natural
transition orbitals strategy. While these tools are often introduced
separately, we decided to formally detail the connection existing between the
two paradigms in the case of excited states calculation methods expressing any
excited state as a linear combination of singly excited Slater determinants,
written based on a single-reference ground state wave function. In this
context, we show how the molecular exciton wave function plays a central role
in the topological analysis of the electronic transition process.
