Want to learn MVC in PHP, where to start? What framework to choose for a project?

Try Yii — compact, a promising framework, there is a Russian documentation and forum.

Most likely call a lot of objections, but if you can spare the time to understand MVC, I would advise to start writing a project without any framework.
Let me explain why.
When I started to deal with PHP frameworks had been developed, the subject had no great popularity. And the level I got was not the one to understand such a structure. And, like most beginners, I began to reinvent the wheel. Made one website. During the expansion it turned out that some space to expand strongly uncomfortable. Thought, looked at the source code of other projects (then it was a forum IPB 2), some architectural decisions have borrowed, but without understanding their essence. Then first heard about the frameworks, saw some finished pieces of my code can execute and allocate in its own platform. I already knew about OOP, I began to read the patterns of the big four. In the course of development often fell into the same trap, rewrite entire subsystems, some moments looked at existing frameworks, with each mistake came to understand why in serious platforms made by "so and not otherwise". Eventually it got to the point when my "framework" needed to redesign from scratch and it would then become very easy to use, very extensible and General... And at the design stage, it is understood that all is already written to me and me to write anything of meaning anymore. Only by this time I knew, it understood and didn't know many of the techniques used in MVC frameworks. And as General they are similar, the time learning new frameworks was significantly reduced by understanding how they work. Many moments are clear, just the source code and use cases, without documentation.
Yes, it will take a lot of time, but no problems with the change of the framework. And Yes, even language. Its first application on Rails after meeting with him (before this ruby generally was not the case), I wrote for three days, starting with "how to install Ruby". It was the interface of inbox is a mailbox with a bunch of Ajax and all sorts of Goodies like search, filters, and other things.
So, of course, if you have time and desire, I recommend to either try to write your bike, or to a full understanding of deconstruct any ready framework, then it does not matter what.

Zend Framework — bulky, large, slow — but as an example, since the PLO systems is perfect. A lot of examples of a huge community.

www.symfony-project.org/ — also one promising framework... brainfuck a little at first, but fine... )

I would suggest by far the Zend as the Swiss knife that can cut any desired item of decent quality, but! But the assaults to understand is not easy, so you should start with a kitchen knife, the simplest lightweight analogues of type CodeIgniter (good dock, clear structure, easy transition with him on Zend). As for MVC, so it's a trend, and it is implemented in almost all modern frameworks.

cakephp for small projects. Not the most nimble of course, but in my opinion well implemented MVC, a clone of the ruby...
Documentation is excellent, in Russian.
A lot of things implemented in the game.
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\rcakephp habré, Google group
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It is also worth to look at kohana
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Yii and Zend have already recommended...