Normally 再 is a subjective term, which is frequently used before you do something again. However 又 is an objective term, which is used after someone has done something again.
As we know, the difference between objective and subjective is the difference between fact and opinion. Facts are objective, and opinions are subjective ideas held by us.
再读一次吧 （subjective, opinion）you just offer your suggestion “it would be better to read it again”
他又读了一次 (objective, fact) you're just stating the fact that he read it again.
In addition, 再 is placed before 能，可以....; whereas 又 is placed after 能，可以....
你能再读一次吗？（you can't say "你能又读一次吗？"）
他又能工作了．（you can't say "他再能工作了"）
“再（也）没（有）/不" means you will never do something again, or you have never done something again since...
从上周六，他再没有见到她．He never saw her again from last saturday or i've never seen her since last saturday.
在上周六，他又没有见到她. He didn't see her again last saturday.