Massive surges of enrollments in courses have led to a crisis in several computer science departments - not only is the demand for certain courses extremely high from majors, but the demand from non-majors is also very high. Much of the time, this leads to significant frustration on the part of the students, and getting seats in desired courses is a rather ad-hoc process. One approach is to first collect information from students about which courses they want to take and to develop optimization models for assigning students to available seats in a fair manner. What makes this problem complex is that the courses themselves have time conflicts, and the students have credit caps (an upper bound on the number of courses they would like to enroll in). We model this problem as follows. We have $n$ agents (students), and there are "resources" (these correspond to courses). Each agent is only interested in a subset of the resources (courses of interest), and each resource can only be assigned to a bounded number of agents (available seats). In addition, each resource corresponds to an interval of time, and the objective is to assign non-overlapping resources to agents so as to produce "fair and high utility" schedules. In this model, we provide a number of results under various settings and objective functions. Specifically, in this paper, we consider the following objective functions: total utility, max-min (Santa Claus objective), and envy-freeness. The total utility objective function maximizes the sum of the utilities of all courses assigned to students. The max-min objective maximizes the minimum utility obtained by any student. Finally, envy-freeness ensures that no student envies another student's allocation. Under these settings and objective functions, we show a number of theoretical results. Specifically, we show that the course allocation under [...]