What is a Theme?

For my first task I need to create a theme and variations. So first what is a theme?

Theme
A melodic figure or phrase that is the basis for a composition or a section of a composition. Themes can and are repeated many times in many different formats and by many different voices or instruments. *Some very good examples of thematic presentation are the closing credits for any and all of the Star Wars movies. The ending music presents all the themes presented in the movie.*(Benjamin Hollis, 2011, http://method-behind-the-music.com/theory/dictionary#T)

I have also found an intresting article in the Encyclopædia Britannica about musical variation.
http://www.britannica.com/EBchecked/topic/399274/musical-variation
and a basic interactive tutorial on theme and variation which is available here:
http://www.erikscull.com/portfolio/assets/flash/variationswcopland.html
Examples of theme:

Lord of the Rings – Howard Shore
The main theme appears many times throughout the film, yet it is rarely exactly the same as the first time it is heard. The first time it is heard the instrument playing is what I believe to be a pan pipe this ties in will the calm and peaceful beginning of the story.
when the fellowship breaks the theme is augmented and played on brass and the melody is rearranged, this time it reflects a sense of sadness. The pipe sound returns at 2’15″ yet it seems more sad than in the beginning of the clip above, this is down to the underlying strings that are of a lower octave and the addition of vocals which are harmonising with the stings.
Batman – Danny Elfman
The notes of the main theme are B, C♯, D, G and finally G♭.
There is a higher pitched arpeggio that can be heard starting at  0’16″ the notes of that arpeggio are G, G♭, D, B. Just from looking back at the notes that make up the main theme it is obvious the arpeggio on the celesta or harp is inspired by the main theme and just reformatted (in fact it is nearly in reverse to the main theme) and use of diminution is used (to shorten the note length).
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