Easy book to understanding basic concepts I have a medium-strong background on programming and logic, however I'm trying to start using R, and other tools to make machine learning based studies of some problems. I did take probability and statistics at university, but it was a very poor taught one and never realized until now.
I found two books on Amazon I liked:


*

*Naked Statistics: Stripping the Dread from the Data

*The Complete Idiot's Guide to Statistics
Both seem like good starting points, at least to quickly understand key concepts and then use different automatic tool techniques for my purposes, but has anyone read those? Which one is better?
P.S. I would like to learn: distributions (normal, poisson, etc), descriptive statistics, inferential statistics, hypothesis, $R^2$, probability, Bayes, Markov chains, and all related concepts.
 A: Given that you are a programmer you probably should not bother with the dummies' style books and take advantage of your skills to simultaneously learn R and statistics. 
I found the most insightful book for the pure programming side of R and as a reference to be
The Art of R Programming.
Great books to get you going on both the stats theory and R are:
Linear Models With R, Extending the Linear Model With R and Generalized Additive Models in order of progression. The three books seem to be built around first thoroughly but succinctly explaining the theory and then getting down to business with some R code. So it should be a good way for you to learn.
If you feel you need more basic statistics and the stats books above seem to be a bit much for you to kick off with, try All of Statistics, Mathematical Statistics and Data Analysis or Mathematical Statistics with Applications. Youtube has plenty of good 101 Statistics courses at a useful level MIT, MIT2, UCIrvine and machine learning courses as well.
For Machine Learning I like Elements of Statistical Learning and Pattern Recognition and Machine Learning.
Of course R has many more aspects than the ones covered in these books but they should keep you busy for quite a while. www.stackoverflow.com has the R programming topic covered. 
This list is subjective and based on personal encounters. It aims to be helpful and does not claim to be definitive in any way.
A: Having read numerous texts in this space, I would highly recommend R by example.
The text has a very broad overview of various statistics concepts, and how to run examples in R. And I agree with Hans post, that a good approach is to tackle both R and Statistics with texts geared towards both.
A more formal text would be Discovering Statistics Using R. While less broad in scope than "R by example", it has a more formal and explanatory approach to many of the core concepts of statistics using R.
However, keep in mind both of the above texts are more geared towards statistics; not machine learning.
There are several good books more dedicated to machine learning, but less dedicated to some of the statistical concepts you describe (like markov chains).
Several good R cookbooks that have more of a coding/machine learning emphasis and more of a hands on applied approach to using R for machine learning are available. Among them, R Cookbook, R in action, and Machine Learning for Hackers are all very good.
A more recent text that is very good at practical examples for ML/data mining is Data Mining and Business Analytics with R; it is a bit costly, but one of the best practical example books (specifically dedicated to data mining/machine learning) I've come across.
Lastly, a more recent book in the cookbook space that is good is Machine Learning with R. It is very dedicated to ML and R examples, while being a more gentle introduction suitable for those with a programming background.
While Elements of Statistical learning is a great text, I really wouldn't recommend it as an introduction to the field. There is a more recent text by the authors, with a less rigorous introduction, An Introduction to Statistical Learning: with Applications in R. The 2nd text has numerous computational examples to reproduce.
Seeing as you've had prior coursework in statistics, I don't think any of recommendations are too advanced. However, the "Naked guide to statistics," is more of a layman's general audience non-fiction book describing Statistics. And the second book, as far as I know, lacks R, and is likely too broad and dense with sparse examples (haven't read it though).
You can preview many of the books on amazon (7 days) or portions on google books, to see if they are suitable to you.
A: Adding to the other great books mentioned, I would suggest Modern Applied Statistics with S-PLUS by Venables and Ripley. Since you want to learn R (that is based on S) and statistics at the same time this is a very good resource. It may seem pretty outdated but it is a great introduction to many modern statistical methods providing both short introduction, examples and instructions on how to use S-PLUS (in 99% of cases it works the same in R) for estimating those models that guides you step-by-step through data preparation, estimating the model and assessing model fit. It is a practical resource for learning applied statistics but for catching up with theory you would need other books (already mentioned by others).
A: Here is a good collection of books in probability and statistics including R programming. Stay away from "dummies" or "idiots" guide type books because (I think) they needlessly dumb down concepts in an attempt to fast-track a reader, whereas what you really want is material that makes you invest time in learning which gets you thinking on your own. HTH
