Data Science books

What is data science and what you need to know to be a data scientist?
Joel Grus, in his book writes “There’s a joke that says a data scientist is someone who knows more statistics than a computer scientist and more computer science than a statistician. (I didn’t say it was a good joke.)”

Data Science from Scratch: First Principles with Python by Joel Grus
Doing Data Science: Straight Talk from the Frontline by Cathy O’Neil and Rachel Schutt
Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython by Wes McKinney

Machine Learning
Artificial Intelligence: A Modern Approach by Stuart Russell and Peter Norvig
Introduction to Machine Learning by Ethem Alpaydin
Introduction to Machine Learning by Alex Smola (free download)
Pattern Recognition and Machine Learning by Christopher Bishop
Programming Collective Intelligence Toby Segaran
Bayesian Reasoning and Machine Learning by David Barber
Bayesian Data Analysis by Andrew Gelman and John B. Carlin

Data Analysis
Data Analysis Using Regression and Multilevel/Hierarchical Models by Andrew Gelman and Jennifer Hill
The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Trevor Hastie and Robert Tibshirani
Statistical Inference by George Casella
Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi (draft free download)

Statics and Probability
Introductory Statistics Barbara Illowsky,Susan Dean (free download)
OpenIntro Statistics by David M Diez, Christopher D Barr, Mine Cetinkaya-Rundel (free download)
Introduction to Probability by Charles M. Grinstead and J. Laurie Snell
Introduction to Probability Models by Sheldon M. Ross
A First Course in Probability by Sheldon Ross

Linear Algebra and Calculus
Active Calculus Matthew Boelkins, David Austin, Steven Schlicker (free download)
Convex Optimization by Stephen Boyd and Lieven Vandenberghe (free download)
Linear Algebra and Its Applications by Gilbert Strang
Linear Algebra by Jim Hefferon
Linear Algebra by David Cherney, Tom Denton and Andrew Waldron (free download)
Linear Algebra Done Wrong by Sergei Treil (free download)

Presenting the information
The Visual Display of Quantitative Information by Edward R. Tufte