The Kourovka Notebook is a collection of unsolved problems in group theory.
It’s stunning. If you like group theory, you owe it yourself to check it out. Infinite group theory is alive and well. So many cool problems (some have solutions, but many are still open). The book is free. Dr. Mark Sapir (Vanderbilt) informed me of it when I posted the following question on MathOverflow:
Does there exist a rational number 
