The ever-increasing population living near active volcanoes highlights the need for the implementation of effective risk reduction measures to save lives and reduce the impact of volcanic unrest and eruptions. To help identify volcanic systems associated with potential high risk and prioritize risk reduction strategies, we introduce a new Volcanic Risk Ranking (VRR) methodology that integrates hazard, exposure, and vulnerability as factors that increase risk, and resilience as a factor that reduces risk. Here we present a description of the methodology using Mexican volcanoes as a case study, while a regional application to Latin American volcanoes is presented in a companion paper (Guimarães et al., submitted). With respect to existing strategies, the proposed VRR methodology expands the parameters associated with hazard and exposure and includes the analysis of 4 dimensions of vulnerability (physical, systemic, social, economic) and of resilience. In particular, we propose 41 parameters to be analyzed, including 9 hazard parameters, 9 exposure parameters, 10 vulnerability parameters and 13 resilience parameters. Since the number of parameters evaluated for each risk factor is different, they are normalized to have the same weight based on dedicated sensitivity analyses. In order to best illustrate the methodology, the proposed VRR is here applied to 13 Mexican volcanoes and compared with other approaches. We found that the volcanoes associated with the highest combination of hazard, exposure and vulnerability (3-factor VRR) for this geographic area are Tacaná and El Chichón regardless of the analyzed time window of eruption occurrence (i.e., <1 and <10 ka). Nonetheless, the volcanoes with eruption <1 ka that require the most urgent actions as associated with no or few resilience measures in place are Michoacán-Guanajuato Volcanic Field and San Martín Tuxtla (4-factor VRR); the top volcanoes in the 4-factor VRR with eruption <10 ka are Michoacán-Guanajuato Volcanic Field and Las Cumbres.