what book about neural networks or AI in general would you recommend? Which one is the best to learn about this topic from scratch? It would be awesome if it contained also information about the latest discoveries from this field.
Some people might take issue with this, but as far as resources/classes/research groups in academia/textbooks go, AI != machine learning. And neural networks are a subset of machine learning.
The AIMA book is the best introduction to AI, but only to traditional AI, which consists mostly of planning/search/inference algorithms (brute force algorithms, albeit clever brute force algorithms). It is not a book on machine learning, even if it talks a bit about machine learning.
The Deep Learning book that people mention is not an introductory book on the subject of neural networks or machine learning.
Your best bet is Andrew Ng's Coursera course as an introduction to ML and neural nets.
For something lighter but insightful, Pedro Domingo's The Master Algorithm is quite fun.
A great number of classes are now available online. I prefer the Stanford classes. http://cs229.stanford.edu/ and http://cs224d.stanford.edu/ are good places to start. There are more.