-  Pattern Recognition and Machine Learning (Information
Science and Statistics)
-  The Elements of Statistical Learning
-  Reinforcement Learning: An Introduction by Barto and Sutton
-  The Deep Learning by Aaron Courville, Ian Goodfellow, and Yoshua Bengio
-  Neural Network Methods for Natural Language Processing (Synthesis Lectures on Human Language Technologies) by Yoav Goldberg
Then some math tid-bits:
 Introduction to Linear Algebra by Strang
-  [PDF](http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%...)
-  [amz](https://www.amazon.com/Reinforcement-Learning-Introduction-A...)
-  [site](https://www.deeplearningbook.org/)
-  [amz](https://www.amazon.com/Deep-Learning-Adaptive-Computation-Ma...)
-  [pdf](http://incompleteideas.net/book/bookdraft2017nov5.pdf)
-  [amz](https://www.amazon.com/Language-Processing-Synthesis-Lecture...)
-  [amz](https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-S...)
For the former, I would recommend Hands-On Learning with Scikit-Learn and Tensorflow
As a scientist coming to deep learning from another field, I found Courville et al to be pitched at the perfect level.
ISLR introduces you to many of the same topics in a less rigorous way. Once I was familiar with the topics and had worked through the exercises, Elements became much easier to learn from.
I'm not sure if reading Introduction will prepare you for Elements so much as it will just give you some knowledge you can use and see if it makes sense for you and what you want to do to go and (re)learn some of the math tidbits that you need for Elements.
His blog, http://www.fharrell.com, also contains interesting posts.
People seem to love this textbook - and understandably so because it's very approachable. But I really struggled with how informal the tone was, and how friendly it was. Perhaps I'd grown too accustomed to the typical theorem -> proof -> example -> problem set format.