The best way to think of the Jazz Melodic Minor scale is as the Major Scale with the 3rd note lowered by a half step. As the name suggests, this scale is used extensively in Jazz (as are many other scales!). If you have not done so already, I highly suggest you take a look at the Harmonic Minor lesson. These two lessons really go hand in hand. And if it wasn't for the fact that there are 14 exercises between the two lessons, I would combine it all into one lesson. But my goal isn't to fry your brain (just your fingers!).

When practicing these scales, be sure to use the scale patterns from the Diatonic Scale Patterns and Sequences lesson. Also, as you are playing, notice that these modes don't get you the exotic sounds like the Harmonic Minor modes do (Spanish, etc). They get you a ... well, Jazzy sound!

The Jazz Melodic Minor scale is a Dorian-esque scale. It is often used over all altered Dom7 Chords, and it is also common to use the scale one half step higher than the Dom7 chord you are playing over (i.e. use Ab Jazz Melodic Minor over G7).

Here we see how similar the shape is to the Dorian mode. The only difference is that that here the 7th note is raised.

Use the same approach here as with the Harmonic Minor exercises. First, just play the scale up and down as shown in the tab. But after you get comfortable with it, mix it up with the associated Major mode. For instance, ascend with the Jazz Melodic Minor, and descend with Dorian.