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I am learning some Bach inventions at the moment, right now it's the BWV 773 C minor.

I am just learning it by breaking it into sections, hands separate, hands together, slow tempo etc.

But knowing Bach, he probably had specific technical lessons in mind with each of the inventions, apart from learning contrapuntal playing and composition.

Is there a guide online (or elsewhere) that describes the "point" of each invention, what to focus on when practicing a specific invention?

Each one is a different genre. Can anyone name some?

In the notes in my Inventions book it says (for the No.2 in C minor):

"A much more complex and difficult work than its predecessor. The lengthy canons and sinuous lines, very reminiscent of an Allemande, must be spun with care, while the many ornaments prove quite taxing, particularly to the left hand. In my own performance I have found inconspicuous pedaling and varied articulations helpful, though both ingredients require a great deal of contemplation. Collisions between the hands are a frequent issue, and I have indicated in several places fingerings than can help with disentangling".

This is from Schirmer's Performance edition, edited by Christopher Taylor. Hope that helps a bit, sorry I don't have a more comprehensive resource (though there are performance notes for each piece in the book).

Also, whilst not specifically an "instruction guide" for the Inventions, this is a pretty good article in general on performance of baroque music:

Elements of Baroque Performance Style as Applied to JS Bach

I particularly find the discussion on scale fingering interesting: we assume scales have always been played as we play them now, but that's clearly not the case and perhaps understanding the preferred fingering of the composer might help better perform their music authentically?

Check out An Analytical Survey of the Fifteen Two-Part Inventions. It's expensive!! but very in-depth.

Here is a dissertation on the two part inventions:

THE TWO-PART INVENTIONS OF J. S. BA...FORMANCE PRACTICE OF BACH AND HIS CIRCLE

It's very comprehensive. I'm still reading......

I got my library to buy the book and read the Phd some years ago. Interestingly, neither answers the blatantly obvious question of the differing genre. Cathryn thanks for the Allemande for no. 2.

http://www.pianostreet.com/smf/index.php?topic=10500.0

Wow! Bernhard used to be here too I think. Many answers from him (below) but still there's more refinement that can be done. Bach was showing not just how to compose but how to compose in differing genre.
No. 1 – Vocal
No. 2 – Vocal
No. 3 – Vocal
No. 4 – Keyboard
No. 5 – Keyboard
No. 6 – Vocal & dance (Courante)
No. 7 – vocal
No. 8 – keyboard
No. 9 – vocal
No. 10 – Dance (giga) & keyboard
No. 11 – vocal & keyboard
No. 12 – Dance (giga) & keyboard
No. 13 – Vocal & keyboard
No. 14 – Dance & keyboard
No. 15 – Dance & vocal.

Thanks anamnesis. It occurs to me as I see Mayla's dots there - will they become as infamous as his posts wise?

I think probably the best "guide" you could find for the Inventions would be a really fine piano instructor.

There is no right or wrong approach. The piano didn't exist in Bach's day, so don't stress out about correctness, just follow your ear. The academic approach to playing Bach on the piano is to pretend you are playing the clavichord or harpsichord which had no dynamics or pedals. This is obviously extremely childish and short sighted given that bach would certainly not do it himself. His range of dynamics and rubato when playing a keyboard instrument with dynamics, ie the organ, was incomparable and wild. Oddly enough, just like every great composer.

As far as the ourpose of the pieces, the is no technical idea behind them, they are not etudes in the Chopin sense, because that had not even been invented yet! They are mearly examples of good writing for his students, not meant to be performed at all, and certainly not keyboard exercises, but rather composition studies. And yes, they each follow a different form. Look at #2, it's easy to see it is a strict canon, for example (the LH copies the RH a bar later)
Have fun!

I would hope that is not the 'academic approach' as the clavichord, which would have been played by the majority of his students and was, according to his son, his favourite instrument, had plenty of expressive capabilities. Here's one I posted in another thread: https://soundcloud.com/budscott/wfbach-polonaise-in-e-minor