This study aims to investigate undergraduate Mathematics students’ difficulties with mathematical proof in their first encounter with Abstract Algebra. Abstract Algebra, and Group Theory in particular, is one of the most demanding mathematical fields for novice students, due to its abstract nature. This difficulty appears to have an unfavorable consequence on the proof production. For the purposes of this qualitative study, there has been used the Theory of Commognition. Analysis suggests that proof is considered a difficult task mainly due to students’ incomplete grasp of the newly introduced algebraic notions, and due to problematic application of the various proving strategies. This difficulty has often a negative impact on students’ engagement with pure Mathematics in general, resulting novice undergraduate students’ tendency to avoid the study of other Pure Mathematics modules.