This problem is equivalent to finding the topological order in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.

<a href="https://www.youtube.com/watch?v=ozso3xxkVGU" target="_blank">Topological Sort via DFS</a> - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort.

Topological sort could also be done via <a href="http://en.wikipedia.org/wiki/Topological_sorting#Algorithms" target="_blank">BFS</a>.