I'm still pretty new to generalized linear models, and I struggle with a lot of the notation in most of the GLM texts I've picked up. Are there extremely popular GLM books that lend themselves better to readability?
For a new practitioner, I like Gelman and Hill.
Ostensibly the book is about Hierarchical Generalized Linear Models, a more advanced topic than GLMs; the first section, though, is a wonderful practitioners guide to GLMs.
The book is light on theory, heavy on disciplined statistical practice, overflowing with case studies and practical R code, all told in a pleasant, friendly voice.
I am a big fan of Agresti's Categorical Data Analysis.
I have read Agresti's Intro book but found it missing key interpretations for how generalized linear model is built and how it works. For example, you may not need to know how the binomial distribution and logit link work if you only want to fit a logistic regression. However it is annoying when you have read the chapter and started to wonder about it but couldn't find it in the book.
The McCullagh and Nelder GLM book is hard to read. It contains everything you need to know but lacks the derivation for the key results.
Luckily Agresti's Categorical Data Analysis presents a good balance.
As a complete beginner myself, I found Foundations of Linear and Generalized Linear Models by the celebrated author of Categorical Data Analysis Alan Agresti to be helpful. Language is fluid, though some exposure to Linear Algebra is assumed.
I really liked Mixed Effects Models with Extensions in R - Zuur, et. al. It's a followup to their older book Analysing Ecological Data (2007). They do a good job of motivating the models, along with plenty of visual examples to explain what GLMs look like. They also strike a good balance between, theory, application and discussion. Plus they have all codes and datasets on their website, so you can immediately apply what you've learned.