This book reports on first year undergraduate students' difficulties in proof construction in the area of set theory. The study adopted a Purposive sampling where a total of 73 respondents were selected of which 67 were first year Mathematics students and 6 were their lecturers. Data were collected using two instruments i.e. a test for students and questionnaire for students and lecturers. The data gathered were analyzed to explore difficulties faced by first year Undergraduate students when constructing proofs in set theory. The findings from the study showed that first year students had difficulties in construction of proofs in set theory. This was from the incorrect answers obtained in the test questions given where 45 students representing 67% failed question one, 35(52%) students failed question two and 40 students representing 60% failed question three.