Deep LearningAn introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors. 
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Super..cool
These are comments which I've read in other reviews, however, I definitely agree with them.
I have a Bachelor in Science in Mechanical Engineering with a Minor in Statistical Quality Control and a Master in Science in Sustainable Energy Technologies. I'm not bragging about it. I just want to make clear I have a strong mathematics and statistics background.
After reading books like Introduction to Statistical Learning, Introduction to Machine Learning with Python and Python for Data Analysis and taking Andrew Ng's machine and deep learning specializations in Coursera, I thought it was a good idea to have a text book to follow upon what I learned with all the very valuable resources I mentioned.
Andrew interviewed Goodfellow and Bengio in his online courses and given the size of their contributions to the deep learning community, I thought there were no better people to write a book about this incredibly influential field. Unfortunately, the result is a highly technical book in which even the introduction is hard to totally grasp. If you are not very familiar with matrix calculus, and in particular with matrix calculus notation, you're going to have a very hard time with this book.
Something I appreciated from the aforementioned books is that all the authors found a way to explain in a very down to earth manner (as down to earth as this very complex subject allows) what each algorithm is doing and how it's searching for an optimal result. That doesn't happen in this book.
According to Goodfellow, this book is meant for undergrads and postgrads alike. Nevertheless, if you are not able to read and fully understand a common math Wikipedia article (say Gini coefficient, for example) like myself, you're probably going to find yourself in a position in which you may be even more confused relative to how you started.
I eventually gave up around page 150. I referred to some isolated subjetcs from time to time (convolutional networks, sequence models, GANs, etc.) and sometimes it was useful. It wasn't most of the time, though.
If you read the book's critics on the back, you'll notice amazing opinions from Geoffrey Hinton, Elon Musk and Yan LeCun. That may encourage you to buy it, but please take into account these are no 'normal' human beings and what may seem obvious to them, could very well be quite complicated for an average mind, specially if there is no mathematical background involved.
Bottomline, if you are very well versed mathematically speaking, this may be the best book available. Otherwise, you may be better off trying some online material such as Andrew Ng's excelent set of specializations.