This is just some of my collection, any one of which would get you started, but I'd start with Dr Stevenson's stuff first:
Dr Ian Stevenson
Dr Loell Whitton
Dr Raymond Moody
Dr Edith Fiore
Plus I'd check out this four part Documentary
Special Thanks to u/malibunyc for finding a low res 640x360 version of the show on YouTube, here are the links:
ep 1 - https://www.youtube.com/watch?v=u9bcNeLJTv8
ep 2 - https://www.youtube.com/watch?v=ycwZTYHqqoM
ep 3 - https://www.youtube.com/watch?v=PkcljsaaFXs
ep 4 - https://www.youtube.com/watch?v=5URv5xxSFpo
Hope these help. I am looking into the possibility of uploading my personal HD copies of it somewhere but DRM is a bug bear.
There isn't incontrovertible proof and probably never will be, but there is some good evidence presented by Ian Stevenson (a professor from the university of Virginia) and his team of researchers. They found a lot of cases of children who seem to remember details of a previous life. Details they couldn't have known from experiences involving their five senses.
If the Hannah Monsour/Suzanne Ghanem case is to be believed, that's as close as we'll get to proof, but there are lots more cases. One case allegedly led to a murderer being exposed ad confessing his crime.
Ian Stevenson wrote a few books (UK Amazon link - US link here) you might be interested in if you want more info. He has videos on YouTube as well.
Oh, I'd also check out the 4 part documentary: Life, Death and Reincarnation, which unfortunately can now only be found on Youtube in a low res version:
Thanks to u/malibunyc for finding a low res 640x360 version of the show on YouTube, here are the links:
Hope these help.