What Does Judaism Say About Reincarnation?

Today soul reincarnation is widely accepted as both true and consistent with Jewish sources (there are still some holdouts).

Thinking otherwise is considered by many Jews to be heretical (a ridiculous proposition!).

The Rashash Baba Metzia 107a says:

גמ’ שם, מה ביאתך לעולם בלא חטא. מכאן סתירה קצת לבעלי דעת הגלגול

Find a summary of the proof-texts in favor of reincarnation in Devar Yaakov (on Shas) Baba Metzia idem (at the end).