Group codes over fields are ideals in the group algebra KG, where K is a finite field and G is a finite group. Introduced by Berman and MacWilliams in the late sixties as a generalization of cyclic codes, they are still the subject of intense research. This short course is intended to be an introduction to their theory, presenting their main properties in relation to classical codes. The last part of the lecture will give an overview of current research perspectives and open problems. A good reference (among the rare ones) for these codes is Chapter 16 of the recent Concise Encyclopedia of Coding Theory by Huffman, Kim, and Solé.