"Artificial Intelligence: A Modern Approach" (AIMA) by Russel and Norvig is a general introductory book on AI. That means it not only covers sub-symbolic AI (like machine learning) but also symbolic AI. Therefore, it can "only" give you an overview of each topic (I put only in quotation marks since it is actually quite ambitious to cover all topics of AI in a single book!).
Regarding the topics you have mentioned that means:
- you will have read about the basics of neural networks but will not have seen much about deep nets (the 3rd edition only has 10 pages on neural networks, i.e. it's really basic)
- you will have read the basics of reinforcement learning (the 3rd edition has 23 pages on this, i.e. it's basic but more comprehensive than neural networks and enough to read papers about the topic)
- you will not have read anything about NEAT but have read about the basics of genetic algorithms and neural networks which NEAT is based on (and can read the corresponding papers afterwards)
So, regarding your preferred topics, AIMA is one way to get started if you're not only looking for a selectively deep but also a broad understanding of AI. The road could go like this:
- Read a general AI book, e.g. AIMA
- Read a general ML book, e.g. "The Elements of Statistical Learning" by Hastie, Tibshirani, Friedman
- Read deep dive books on selected topics, e.g. "Deep Learning" by Goodfellow, Bengio, Courville
- Read papers for your topics of interest, e.g. "Mastering the Game of Go without Human Knowledge" by Silver et al.
The quicker start would be of course to start at step 2 or 3 and only go to previous steps to look something up if it is required.