This is a very quick pointer to three books that I like and they are known as classics or classic-to-be's.
My Top 3 are all free!
They are all available by their generous authors for free and they can also be purchased from Amazon.
EVERY scientist should read this!
I personally started with "An Introduction to statistical learning" (ISL) by Hastie & Tibshirani. This is a book that every scientist needs to read at least the first few chapters of it.
This book is aimed at upper undergraduate level students or PhDs from non-mathematical sciences. The other benefit of it is that it teaches you R programming language, which is extensively used in the data science community.
Learn the Basics from Classics!
From the same authors comes the second good resource, The Elements of Statistical Learning which is the more advanced version of their other book. It is an interesting read, highly recommended.
Based on your level of knowledge you can skip the first book and start from the second book (ESL).
Deep Learning is HOT!
Deep learning has got a lot of attention and hype. Mostly through its highly successful applications and good publicity! Ian Goodfellow and Yoshua Bengio have written a great book, Deep Learning, on the topic that was published December 2016. The first part of the book has a nice review (and pointers) to the basic mathematical concepts such as linear algebra, probability, and information theory. This book is a pleasure to read for me.
After this is all about reading papers because AI and Machine Learning are growing at a great speed so it is very hard to keep up with the state of the art.
If you are a life long learner, jump in, read, and code!