I am very interested in learning piano but more specifically jazz. I really like the way people can just improvise. I know that I would not be easy but I would like to know what the best book or specific resource I can learn to learn jazz improvisation. I'm not too interested in playing any specific piece of music. I purchased a 61 key digital keyboard and I am a complete beginner; I know nothing about how to play piano or any instruments.
This is on its way to being closed, but it sounds like you need, first and foremost, a teacher. You say you know nothing about how to play any instruments - piano included.
There's always two distinct parts to learning music on any instrument. There's the instrument itself - how it produces the sounds, and there's the music - a huge subject on its own, which has only some relationship with the instrument concerned.
Since piano is one of few on which chords and melody can be played simultaneously, there's a lot to do before even considering playing jazz on it.
Start simply, by just messing about and learning what a piano is about. It may be that with a 61 note instrument, there's no 'piano' action. In which case, you're looking at changing it quite soon. Learn about triads, developing into more complex chords. learn about pentatonics, and how they will ease you gently into improvising. There's a start for you, but requests for resources themselves are offside on this site.
You were able to type that question, because you can improvise - in natural language. Written language at least, apparently, but most probably spoken language as well.
The skill of improvisation in music comes the same way as improvisation in natural language: by hearing and mimicing existing expressions. First you just try to copy and repeat what you hear, and then you'll start to make your own combinations and modifications, and the expressions, words, syntax, sentence structure, becomes part of your vocabulary and just knowing the language.
All aspects of music can be improvised: melody, harmony, rhythm. And improvisation of all of those aspects is learned the same way: by repeating existing pieces of music and combining the learned parts in new ways. "Jazzing up" a song means modifying the harmony, melody and rhythm in interesting and creative ways.
Start off by playing simple melodies by ear, in the key of C, so you can start with the white keys only. Then learn to accompany simple songs with chords. Then combine parts of songs and chords in new ways, modifying the songs, making your own variations.
But do try and find a teacher. There is a wide array of skills to obtain, starting from something as trivial as finding where C is on the keyboard. What is a C major chord. Etc.
not too interested in playing any specific piece of music.
Your path to learning improvisation will consist of playing specific pieces of existing music, or at least parts of existing pieces, because that's how you build your musical vocabulary.
It's a long road. I'll just add some points that helped me (note each of these are long topics, I'm just give my short thoughts on them):
You need to understand basic music theory. If you can take a basic music theory course or go through a book chapter by chapter, that will help. There's a lot of information here that musicians take for granted, what the notes are, what chords/triads are. What the major scale is. Part of this is learning to read music. There are a lot of great musicians that don't read music, but learning to read music will make everything much easier imo.
Think of music as melody, rhythm and harmony. This may seem trivial but it was a bit of a revelation to me. Before I realized this I used to think of music more as a bunch of different polyphonic lines that magically worked together (like Baroque music). But for improvisation, it really helps to divide music into melody, rhythm and harmony. Now this basically means that you have a melody line (the part you sing) and you have a "chord" behind it. So a song is a sequence of chords in the background, with a melody in the front.
On the piano this (very basically) translates to a chord in the left hand and a melody in the right hand. Then you can eventually add a third element... a bass line which acts as part of the harmony and rhythm.
So you have these 3 parts... a melody, a bassline, and chords. But you only have 2 hands. The art of solo jazz piano is to get these 3 parts work together with your two hands. Sometimes you leave out the chords, sometimes you leave out the bassline. It's all a matter of taste.
Eventually you want to take a simple tune like 'Happy Birthday' and play it on the piano with a chord in the left hand the melody in the right hand.
Get used to singing melodies, and improvising around them. Take simple tunes like Happy birthday or mary had a little lamb... Improvisation is basically singing lines "in your head" while playing them on the instrument. The easiest instrument to start out with is your own voice.
If you can improvise by singing around the melody of Happy Birthday, then go back to the piano. Again play the chord in the left hand and the melody in the right. But this time try improvising around the melody in the right hand.
To get into jazz you need to learn chords beyond triads. Mainly 7th chords (major 7th, minor 7th, dominant 7th).
Eventually get a "fake" book eg: the Real Book. These are notated with chords and the melody. These books are really suited for jazz players/improvisers. They don't give note for note instructions to the player. You take the chords and melody and play them in the way that suits you.
The technique of the instrument. You need to learn proper fingerings so that you can play fluidly... learning the proper fingerings of scales really helps. But different people have different sized hands, so you may have to find something that isn't the accustomed fingering that suits you. You want to minimize stress on the hands and shoulders etc. You want to minimize any tension.
Listening to the original songs of jazz standards first before they are "jazzed" up, so that you know the melodies. Then listen to jazzed versions from the 20s and 30s. Why I say from the 20s and 30s is because the improvisation isn't too complex for the ear. In the 40s we get Bebop and the improvisation (imo) takes a quantum leap.