Copyright matters for students
You will require permission from the copyright owner if you want to copy (other than to another format for your own use e.g. CD to MP3), record, download, distribute, or perform music.
Fair dealing for research & study does apply to music, but only in the context of your university study: you may be able to use a ‘reasonable portion’ of a song for instance in a multimedia work created for assessment in a unit or course; but you could not then put that work online, show it in a festival or competition, or as an item of your résumé, without seeking permission to use the music.
Permission to go beyond ‘fair dealing’ - if you want to be able to upload your work to your own website for instance - can be sought through the several collecting societies, APRA, AMCOS, ARIA, and PPCA, who represent copyright owners, music publishers, and sound recording companies.