Core Animation: Simplified Animation Techniques for Mac and iPhone Development
By Quartz, you probably mean Core Animation. Quartz is simply the Mac / iPhone 2-D drawing API, where Core Animation handles animation of views and layers.
It is very difficult to use OpenGL for performing custom animations on views, but Core Animation is designed for this purpose. It has been my recommendation to people that if they are thinking about doing 2-D animations, even in games, they should look at Core Animation first and go to OpenGL ES only if Core Animation's performance is unacceptable. Core Animation lets you do a lot with just a little code, and there are now plenty of great references out there on the topic (such as Marcus Zarra and Matt Long's new book).
You may wish to refer to some of these other questions for more:
When it comes to Core Animation and UIView animations, you might want to look at Marcus Zarra and Matt Long's new book Core Animation: Simplified Animation Techniques for Mac and iPhone Development. It provides a very thorough walkthrough of Core Animation, from the high level UIView animations to more complex animations involving CALayers and CAAnimations. Bill Dudney also has an excellent Core Animation book.
As far as official documentation, the Core Animation Programming Guide is also well-written.
There are many questions here on Core Animation, tagged with core-animation.
Matt Gallagher has an interesting series of articles entitled "An Asteroids-style game in Core Animation".
Finally, I teach a course on iPhone development, in which I devoted a class to Core Animation and the neat things you can do in it. The course notes are available for download (VoodooPad format), and have quite a bit of detail in them, in addition to links to other resources and sample applications.
For this, I'd first recommend reading the Quartz 2D Programming Guide. It's the best set of documentation you'll find out there on the subject. Next, I'd read through some of the questions here tagged core-graphics, quartz-2d, or quartz-graphics. There are some great source code examples in the answers to those questions.
There are many "getting started with OpenGL ES" questions here, with links to many resources. These include:
I personally recommend the book "Mobile 3D Graphics: with OpenGL ES and M3G", as well as the "OpenGL ES Programming Guide for iPhone OS". My application Molecules is open source and it uses OpenGL ES. Finally, Jeff LaMarche has a great tutorial series on OpenGL ES.
By Quartz Core, you probably mean Core Animation. Again, I'd start with Apple's Core Animation Programming Guide, then take a look at the code examples you can find here under the various core-animation tagged questions. Beyond that, Bill Dudney's Core Animation for Mac OS X and the iPhone book is a very good introduction, and Marcus Zarra and Matt Long's Core Animation book looks to go into more detail on the subject.
Here are a couple good and free resources:
Those are couple good books and videos. Also make sure to check out Ray Wenderlich's site; it contain's many good, complete tutorials for beginners. Hope this helps!
In addition to the books suggested by Alex and nevan (of which I'd recommend Marcus Zarra and Matt Long's newer Core Animation book, given its greater quantity of iPhone coverage), I taught a class on iPhone Core Animation recently. The video for that class can found on iTunes U. My class notes, with detailed coverage of Core Animation, can be downloaded here (in VoodooPad format).
I also gave a presentation on Core Animation at the recent iPadDevCamp in Chicago, for which the slides and sample code can be found here.
Core Animation: Simplified Animation Techniques for Mac and iPhone Development explains it nicely.