One of the best-known books on statistics is now free
Larry Wasserman’s All of Statistics is free to download from Springer
I like this book because – unlike most books on statistics - it takes a modern approach to statistics and covers statistics and computer science holistically.
In doing so, it covers a much broader range of topics (hence the name).
However, the book is also quite readable because the author says ‘Rigor and clarity are not synonymous’
Hence, it strikes a good balance
Part I is concerned with probability theory
Part II is about statistical inference, data mining and machine learning.
Part III applies the ideas from Part II to specific problems such as regression, graphical models, causation, density estimation, smoothing, classification, and simulation.
Admittedly, seeing everything in terms of statistics needs some getting used to
Etc etc …
The link again to download is