|| B   D7   | G    Eb7  | Bb     | Am7   D7   | 
 | G   Eb7  | Bb   F#7  | B      | Fm7   Bb7  |
 | Eb       | Am7   D7  | G      | C#m7  F#7  |
 | B        | Fm7   Bb7 | Eb     | C#m7  F#7  ||

I have yet to find a way of noding chords with melody, and when I do, I'll add it. However, the melody here is one note per chord, and is very trivial. Suffice to say that the melody does not make the song, and is not the genius of it. It is the chords that are of interest - and they are what is presented here.
Some music theory
John Coltrane released Giant Steps (both the song and album) in 1959, and with it started a musical revolution. The base of Giant steps is the Coltrane Changes, which you can read about there, but basically - until then, jazz music had been based largely on one tonal center, or on movements of a fourth, or a major or minor second. But no one before had moved the tonality up and down a major third! Coltrane had been working on this harmonic approach for a while, and brought it out with Giant Steps, and also Countdown, on the same album. The thing is, tonalities a major third apart are very different, and it is difficult to move smoothly between them. Giant Steps is, in fact, based on three tonal centers, all a major third apart - B, Eb and G. (If you want, you can view them as Bmaj7, Ebmaj7 and Gmaj7). In fact, it is easy to see that all other chords are just cadences to these tonic chords. D7 is the fifth of G and Am7 - D7 is a II-V progression to G. Likewise with fifths and II-V's to Eb and B. So, stripping away the cadences, and leaving just the tonal centers, we have Giant Steps stripped to:
|| B   G    |      Eb   |        | G          | 
 |     Eb   |      B    |        | Eb         |
 |          | G         |        | B          |
 |          | Eb        |        | B          ||
Which maybe makes it seem a little less intimidating. And it helps see the movement of the tonailities. As you can see, it always moves up or down a major third. This will help if you want to 'scrape through'. A trick you can use is to play the major pentatonic of the fifth of the tonic over the entire tonality. It may sound complicated, but it isn't. You can play D major pentatonic over any chord that is in the 'G tonality' (Am7, D7 or G), Bb major pentatonic over Eb and F# pentatonic over B. Of course, if you do that all the time, you're going to sound pretty boring, so you're just going to have to learn the hard way if you want to sound any good over this. Anyway, it's only II-V-Is (and V_Is). How difficult can it be? Haha.

The thing that makes it so difficult to play over this is that tonal centers a major third apart have few notes in common. For example, G major is G, A, B, C, D, E, F# and Eb major is Eb, F, G, Ab, Bb, C, D. They have 3 notes in common. For comparison - moving a fourth leaves 6 notes in common, and moving down a major second leaves 5 notes in common. And there is not a single note in common to all three scales. Which sucks. You can't even aim for a 'sure' note if you're stuck. Hehe. That was hardly the case before Giant Steps came along. The tonality never flew around like this. Oh, and it's played at almost 300 bpm. That means you have to negotiaite all 3 tonal centers in less than 2 seconds.

Coltrane's recording
Giant Steps is so named because of the bass movement. Usually, the bass moves in steps (whole / half tones) or fourths (as in the common cadence), but here, the bass is moving in minor thirds and fourths (and also tritones). And that is why the piece is called Giant Steps.

Rumour has it that Coltrane practiced virtually nothing but Giant Steps prior to recording it. I am not sure about that, but I do know that at the time, virtually nobody could have played it. Looking at Coltrane's solo, he plays a lot of 'patterns' on the chords. Patterns like 1235 and 1351 (i.e. on B major - B C# D# F# and B D# F# B respectively). With the chords and tonalities moving so fast, it is important to play inside the harmony.

Tommy Flanagan
Tommy Flanagan was the pianist on the recording, and Nat Henthoff, who wrote the liner notes for the album, wrote "Tommy Flanagan's relatively spare solo and the way it uses space as part of its structure is an effective contrast to Coltrane's intensely crowded chorus." What a euphemism! With as much respect as I have for Tommy Flanagan, his solo seriously sucks. But then again, you can't blame him. Nobody can, and nobody has. It was a bit brutal of Coltrane to even think that anyone else could play a solo on it then - and you can hear the strain in Flanagan's solo. It is quite easy to hear that he's not coping at all well with the changes. In fact, Flanagan was quite annoyed at his performance on that particular song. 23 years later, he released an album also titled 'Giant Steps', with his trio. The album had the same songs as the original Giant Steps album he recorded with Coltrane. Probably the reason he did so was to prove to the world that he could play Giant Steps. I personally haven't heard it, but I am assured he did a great job.