Synfig Studio

Synfig Studio is a 2D animation software that uses vectors and rasterized graphics, thus eliminating the need to create animations frame by frame and letting you produce higher-quality 2D animations more quickly and with fewer resources.

Since all the elements are vector-based, you'll only have to worry about pixelation resulting from a change in resolution or size when importing images directly into the program (which is very easy to do).

This tool is compatible with several layer types: geometric, gradients, filters, transformations, and many others. All of them can be handled from the program's interface; that said, more advanced users will be best able to take advantage of all the features offered.

Synfig Studio is a very comprehensive application that comes with an online user manual (found on the developer's website). Use it (with a dose of patience) to create your very own animations.