R. N. Elliott believed markets had well-defined waves that could be used to predict market direction. In 1939, Elliott detailed the Elliott Wave Theory, which states that stock prices are governed by cycles founded upon the Fibonacci-series (1-2-3-5-8-13-21...).

According to the Elliott Wave Theory, stock prices tend to move in a predetermined number of waves consistent with the Fibonacci series. Specifically, Elliott believed the market moved in five distinct waves on the upside and three distinct on the downside. The basic shape of the wave is shown below.

Waves one, three and five represent the 'impulse', or minor up-waves in a major bull move. Waves two and four represent the 'corrective,' or minor down-waves in the major bull move. The waves lettered A and C represents the minor down-waves in a major bear move, while B represents the one up-wave in a minor bear wave.

Elliott proposed that the waves existed at many levels, meaning there could be waves within waves. To clarify, this means that the chart above not only represents the primary wave pattern, but it could also represent what occurs just between points 2 and 4. The diagram below shows how primary waves could be broken down into smaller waves.

Elliott Wave theory ascribes names to the waves in order of descending size:

1. Grand Supercycle

2. Supercycle

3. Cycle

4. Primary

5. Intermediate

6. Minor

7. Minute

8. Minuette

9. Subminuette

The major waves determine the major trend of the market, and minor waves determine minor trends. This is similar to the way Dow Theory postulates primary and secondary trends. Elliott provided numerous variations on the main wave, and placed particular importance on the golden mean, 0.618, as a significant percentage for retracement.
Trading using Elliott Wave patterns is quite simple. The trader identifies the main wave or Supercycle, enters long, and then sells or shorts, as the reversal is determined. This continues in progressively shorter cycles until the cycle completes and the main wave resurfaces. The caution to this is that much of the wave identification is taken in hindsight and disagreements arise between Elliott Wave technicians as to which cycle the market is in.
Here is an example of an Elliott Wave cycle. Ideally, Wave Two would not retrace more than 66%, but you can get a real sense of the wave patterns in action from the chart, just as well.

Read more about the Elliott-Wave: http://www.elliottwave.com/

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