Nearly 20 years since I learnt about GLMs with the first edition of this as a text. I just re-read it and while naturally dated with regard to software and recent developments (regularisation etc) it is still an excellent, clear introduction. I haven't seen recent editions but am sure they are good too. Some linear algebra and calculus required.
An entry level for generalized linear models. The books covers all the essential things you should know about GLM but ignores many necessary details for the beginners. It is a good choice for beginners who want a quick survey about GLM.