Are you taping classes so that you can use the video for subsequent study sessions and review?

If so and you just want reasonable clarity or image quality then my opinion the answer to your question is - Yes!

Two simple ways to do this.
1. Use most any consumer editing program - open the file in the workspace timeline and then select a more compressed/smaller file size to render to - like VCD or SVCD or mpeg1. - Presto - you have a much smaller video file for your study purposes.
2. Use one of many free file transcoding programs - one example is mediacoder easily found via a Google search. Easy to use (sorta) and will one-step transcode your video to most any file type and size.

Final thought for this troubled world we live in be sure your professor/instructor/teacher is aware of and approves of your video taping. Most of those academics consider their lectures and presentations to be their proprietary stuff (the law seems to back them up in this) so be careful what you do with the video. Just mentioning this as now and then in the States I hear of dust ups where students share or even sell notes and recordings and find they are in trouble at University.
goodluck