In this qualitative research, we studied difficulties that undergraduate students face while learning the concept of inner product space. Participants were 35 first-year mathematics students from Yildiz Technical University in the 2011 and 2012 academic years. We asked participants to solve 5 inner product space questions. Data were jointly analyzed by researchers. After evaluating the results, we grouped students' answers into "right," "wrong," or "blank." The foremost difficulty that the students encountered while studying inner product spaces is that they could not understand the concept thoroughly and they did not know how to choose the elements of inner product spaces. Additionally, it was seen that because the students simply memorized the concepts instead of learning and understanding them they made conceptual and procedural errors.