A lot of the time, you'll hear people that claim music theory is not important, or maybe even that it stifles creativity. Often cited are case examples such as Paul McCartney's inability to read sheet music. While it is absolutely true that music theory is not required to write great music, for some people, it can help greatly, and introduce new ways to express oneself through music.

'[t[4]I. The Notes and Keeping Time'[/t]
In Western music, there are 12 '[b]notes'[/b]. That's it. Well, not exactly.
There's a special thing with frequencies and our ears (see Section VII) where, when measured in Hz ('[b]Hertz'[/b], a unit that measures vibration speed), a note with twice the frequency as another seems to work perfectly with it, to your brain. This is called an '[b]octave'[/b].
For example:
Many standards define the note A as exactly 440Hz.
Doubled, this is 880Hz. According to tradition, this note is also A. As is 1760Hz. 
Since our '[b]scale'[/b] is built off of 12 equally-spaced notes, we can derive that a '[b]semitone'[/b] is a twelfth of the difference in Hertz between a note and its octave. A '[b]whole tone'[/b] is two semitones.
The notes are as follows:
A, A# (we will talk about sharps and flats soon), B, C, C#, D, D#, E, F, F#, G, G#

'[t[2]Note Length'[/t]
A '[b]measure'[/b] is a unit in music which defines the length of an arbitrary phrase, sort of like a coherent musical statement. These measures can be and are subdivided, into equal intervals, usually halves, quarters, and eighths.
A '[b]quarter note'[/b] is a quarter of a common time measure (see below). As an example, a 7/4 measure can hold seven quarter notes, while a 2/4 only two.
An '[b]eighth note'[/b] simply takes up half the time of a quarter note.
A '[b]half note'[/b] is twice the length of a quarter note.
A '[b]whole note'[/b] takes up an entire common time measure.

'[t[2]Time Signatures'[/t]
A '[b]time signature'[/b] is the way to express the number of '[b]beats '[/b] in a measure. The most common time signature, and the one most often used in music, is 4/4 (the top number notates how many beats are in a measure, the bottom what length of note makes up a single beat), also called '[b]common time'[/b]. Common time can also be notated as c.

'[t[4]II. Intervals and The Ionian (Major) and Aeolian (Minor) Modes'[/t]

'[t[4]III. Chord Theory'[/t]

'[t[4]IV. Melody'[/t]

'[t[4]V. Uncommon Modes'[/t]

'[t[4]VI. The Science of Sound'[/t]

'[t[4]VII. Timbre and Sound Design'[/t]

'[t[4]VIII. Miscellaneous Tips and Tricks'[/t]

'[t[4]IX. Helpful External Links and References'[/t]