What is the best source to start learning SAS? I'm looking for some book recommendations, video lectures, tutorials or anything that can help me learn SAS.
 A: I found the UCLA website extremely useful, particularly for some of the modeling related tasks that you mention. 
A: I started with "The Little SAS book". It is now in its fifth edition. 
Getting started with SAS is easy with The Little SAS Book.
One of its main feature is that each topic is presented in a self-contained two-page layout: one page with the "theory" and one page with an example.
You can have a look at the table of contents and at a sample of pages via the link above.
This book only covers basic SAS language, but there are many other books for specific statistical topics like categorical data analysis, mixed models, survival analysis, ...
Another interesting possibility: SAS Global Certification program.
A: If you have some background in statistics already, and just want to be able to transition to doing things in SAS that you can do elsewhere, Der & Everitt's Handbook of Statistical Analysis Using SAS is nice.  It's short, simple, fast, and relatively inexpensive.  Note however, that it won't really teach you statistics if you don't know it already.  Neither will it really turn you into a SAS programming expert.  It's best seen as a quick way to transition to SAS, in my opinion.  But, in conjunction with the Little SAS Book, you can very quickly get to the point where you can function in SAS, and begin to move forward on your own.  
A: Based on your comment regarding your objectives, I would likely use a combination of these three resources:


*

*The Little SAS Book: An excellent primer for basic SAS syntax, data handling, etc.

*The SAS documentation for some missing data techniques like Multiple Imputation, as well as some of the various PDFs of papers presented at places like NESUG. This one, for example, in J. Statistical Software.

*Categorical Data Analysis Using the SAS System: A decent treatment of both the code and the statistical underpinnings for things like logistic regression. Alternately Logistic Regression Using the SAS System could also work - I haven't read it, but Paul Allison's survival analysis text is outstanding.

