Below is the the Harmonic Minor Scale and it's diatonic arpeggios.  This PDF is similar to those for the Major Scale and Melodic Minor Scale, so check out those posts if you haven't.  The PDF outlines the Harmonic Minor, it's seven modes and the diatonic arpeggios.

As with the other Scale PDFs, it might be worthwhile to start with the arpeggios for each mode.  Not only are they less notes to focus on, but they are lines in themselves that make succinct, harmonic 'sense' out of the modes.  Once you understand the chord tones for a mode, then you can 'flesh out' the rest of the scale around it.

For the novice jazzer, it is less useful to understand this material for compositional movements, than to just be aware of the arpeggios that are buried within this scale.  While the Harmonic Minor is a great choice for the Min-Maj7 chords and sounds in tunes like Nica's Dream and Nardis, the harmonic minor is probably most used in jazz for altered sounds -- using the Phrygian Dominant over a #11 chord or the Ultra-Locrian for tri-tone colors over a functional Dominant.  Just learning the harmonic scale will give you access to these sounds, but being able to pick out all the arpeggios within it can give you a richer starting point for your lines.

Another key use of the Harmonic Minor in jazz is the 'Barry Harris' approach.  Barry Harris has a whole cosmology of scales and tones that starts with chromatics, splits into diminished and ends with sixth chords.  The 'Barry Harris' scale -- the Major#5 -- is really the third mode of the Harmonic Minor in this PDF.  Check out his 'Sixth-to-Diminished' theory which is at the heart of his teachings.  If you act as if the Third Mode of the Harmonic Minor is the 'One' chord for Major tunes, you can develop a unique perspective into the tunes of the Swing and BeBop era.  Either way, if you are familiar with the arpeggios in the Harmonic Minor and Melodic Minor scales, you will be able to spot them when transcribing the lines of Charlie Parker and other boppers when they go 'outside' the harmony.

Below is a reference for learning the Melodic Minor Scale diatonically.  The Melodic Minor is sometimes referred to as the 'Jazz Minor' due to its applications to Jazz.  You may have gotten hip to the fact that the 7th mode of the Melodic Minor can be used serve up altered sounds over a functional Dominant (a V going to a I).  At some point I also realized that the fourth mode of the Melodic Minor can be used over #11 Dominants.  Learning the totality of the scale with diatonic context of all the arpeggios will give much greater command over these sounds.

While the Melodic Minor only differs from the Major scale by one note, I still find myself struggling to visualize it thoroughly over the fretboard, certainly more than Major scale.  My ability to visualize the Major scale was significantly bolstered by learning all the diatonic arpeggios in the scale, across all the scale 'boxes' where the modes sit with the root on the sixth string.  Learning arpeggios also significantly strengthened my ability to generate lines strongly outlining the harmony. 

You can focus on parts of the neck by breaking it up into 'r6 mode boxes'.  These scale 'boxes' I term with the 'r6' meaning 'root is on the 6th string.'  For instance, 'III-r6' represents the way the notes sit when you play the Phrygian scale with its root on the sixth string.  This lines up as a box, or chunk of the fretboard which is easier to concentrate on, especially at first.

Just like the the Major scale, there are seven notes in the Melodic Minor.  Each of these seven 'degrees' has a mode, chord, and arpeggio associated with it.  Modes are simply the same notes of a scale arranged with a different note serving as the root.  The arpeggio for each degree can be found by skipping every other note in the mode until the next octave is reached.  An arpeggio is basically the notes of a chord played sequentially.

Below are the scales and chords for each degree of the Melodic Minor Scale:

​The Melodic Minor scales are:
I  - Melodic Minor (R, 2, b3, 4, 5, 6, 7)
II - Phrygian #6 (R, b9, b3, 4, 5, 6, #6)
III - Lydian Augmented (R, 2, 3, #4, #5, 6, 7)
IV - Dominant #11 (R, 2, 3, #4, 5, 6, b7)
​V - Mixolydian b6 (R, 2, 3, 4, 5, b6, b7)
VI - Locrian #2 (R, 2, #2, 4, b5, #5, b7)
VII - Super Locrian (R, b9, b3, 3, b5, #5, b7)

The accompanying chords are:
I  - Min-Maj7 (R, b3, 5, 7)
II - Min #6 (R, b3, 5, b7)
III - Maj7 #5 (R, 3, #5, 7)
IV - Dom.7 #11 (R, 3, 5, b7)(#11)
​V - Dom.7 b13 (R,3, 5, b7)(#13)
VI - Min7b5 (R, b3, b5, b7)
VII -Min7b5 (R, b3, b5, b7)
​
I recommend starting with the Melodic Minor arpeggios in the middle section of the PDF.  Take four or five days and run over the arpeggios for one mode (probably start with Min/Maj7) in all the different r6 mode boxes.  Maybe put on a relevant backing track and definitely a metronome.  By the fifth day, you should really concentrate on connecting between the boxes and try to work horizontally or diagonally.

After you have the arpeggios, the scales are just the rest of the notes to flesh them out.  Start with the most useful scales for playing over Dominants, like the Lydian Augmented and Super Locrian.

Finally, learn to run all the arpeggios within a particular mode box.  This will reinforce both the scale pattern and the diatonic progression within the Melodic Minor.

While you are not going to necessarily find a lot of complex harmonic movements of the Melodic Minor in Jazz tunes, learning the diatonics of the Jazz Minor will give you greater facility at minor two-fives and the ability to super-impose these scales in other applications.

Here is a great guide for beginners regarding jazz harmony:

The Ultimate No Nonsense Guide to Jazz Harmony

The contents are pretty much what's labeled on the tin -- straightforward explanations of concepts like:

• II-V-I and other cadences
• Secondary Dominants
• Backdoor Progressions
• Backcycling
• Tags
• Altered Harmony

I made this chart to highlight the Essential Chord Tones (ECTs) for each chord in a diatonic progression relative to the numbers in the Key scale (Ionian Major).  My shorthand for this concept is the "Diatonic Exchange Rate." 

When you play the root of the ii chord, you are just playing the second note of the Key scale.  The third of the ii chord is simply the 4 of the Key scale.  If you think of just these number for each chord in the progression, you can focus on the intervals of the Major scale instead of thinking about arpeggios relative to the Major scale.

I thought this might be helpful to come back to in light of chord solos.  In a chord solo, we have a melody, say on the 'B' string.  For each note we want to accompany with a chord, we have to find at least one ECT common to the chord for the rest of our fingers.  For a ii chord, we would really implicate a minor strongest if we have the flat 3rd of the ii.  Instead of finding the root of the ii and then finding its b3, I would rather just go directly to that note, which happens to simply be the 4 of whatever key I'm in. 

The chords are ordered in 4ths/5ths, common to progressions in Western music.  If you go bottom to top, you are moving in 4ths.

On the second page I grouped the ECTs in order of precedence.  Minors differentiate themselves from Major by virtue of the b3, where as Dominants differentiate by the b7.  You will see a pattern here: moving in 4ths, the third is the seven of the next chord in the sequence.

In the PDF below, I have diagrammed the arpeggios in each 'mode box' for diatonic chords with the 'diatonic exchange rate' pasted on each note.  I excluded the IVmaj7 on the first page for room, but it is diagrammed on page 5.  I also added some extra diagrams for altered dominants.