The second- and third-order algebraic-diagrammatic construction schemes for the electron propagator for studies of electron attachment processes [EA-ADC(2) and EA-ADC(3)] have been extended to include the complex absorbing potential (CAP) method for the treatment of electronic resonances. Theoretical and conceptual aspects of the new CAP/EA-ADC methodology are studied in detail at the example of the well-known 2Πg resonance of the nitrogen anion N2−. The methodology is further applied to π* shape resonances, for which ethylene is considered as a prototype. Furthermore, the first many-body treatment of the π+* and π−* resonances of norbornadiene and 1,4-cyclohexadiene is provided, which have served as model systems for the concept of through-space and through-bond interactions for a long time.