The purpose of this paper was to use APOS theory to analyse undergraduate students’ understanding of proof by mathematical induction against the backdrop of the genetic decomposition. The 2020 class of 159 students wrote a test with three questions on proof by mathematical induction. A further ten students were selected based on their responses to the test to undertake semi-structured interviews. The students’ responses to the test and the interviews were analysed by classifying whether the students had attained the Action, Process, Object and Schema stages of concept-formation. Results indicated that although students operated at all levels of APOS framework, the majority operated on the Action level. Few students managed to attain the desired Schema mental structure. The use of APOS theory gave us a better insight of students’ understanding of proof by mathematical induction, which can help other researchers to make students’ understanding of other mathematics topics.