The following tutorial describes how to create an animated logo like the one below:

Create a Symbol

First create a new Flash document. Add some letters to the stage. In my case I have used my website logo ie. T, M and W at a size of 72 pixels. Select each letter individually and click the F8 button. This will convert each letter to a symbol. Make sure that 'Movie Clip' is selected. Converting each letter to a 'Movie Clip' will allow you to add individual animations to each of the letters. This tutorial only animates the group of letters. Next select all the letter symbols by holding down the shift key and clicking each symbol. Then press the F8 button. Again convert this group to a 'Movie Clip' symbol.

Create Key Frames

Select frame 5 in the timeline and press the F6 key. This will create a key frame at frame 5. Do the same for frame 10, 15 and 20.

Modify Key Frames

Select frame 1. Reduce the size of the symbol by selecting 'Modify' from the main menu and then 'Transform' and then 'Free Transform'. Hold down the 'shift' key while resizing the synbol (this will maintain proportion). Next click on frame 5 and change the image size to be slightly larger. Do the same for frame 10 and 15, gradually increasing the size.

Add Motion Tweens

Right click between each of the key frames and click 'Create Motion Tween'.

Test your animation by holding down the control key and pressing 'Enter'. You should see your logo gradually increase in size. The same concept can be applied to rotation. Try this by rotating the image by 90 degrees in each keyframe.

Finalise the animation by clicking on frame 20 and then selecting the 'Actions' panel for the frame. Type the following code into the code area:

stop();

This will stop your animation once it has played through once.