Reincarnation in the Bible?

In my early twenties I read a book that started me in a completely different direction. Up to that time I had been taught to be agnostic and believed the Bible to be the result of ignorant men trying to explain what they did not understand with superstition, fables, exaggerated history, etc. The book is There is a River by Thomas Sugrue.
A few years ago I started writing down my conclusions in order to clarify to myself just what I did believe. I could not accept the idea that I could be right when everyone I talked to disagreed with me. And yet my conclusions do seem to me to agree with Scripture, including my belief in reincarnation, which I believe is not only a fact revealed in the Bible but is a necessary part of God's plan of salvation.
A motivating factor in my desire to share my understanding of truth is my belief that all of the problems in the world can be traced to erroneous beliefs. If everyone correctly understood and applied truth, I believe our problems would vanish. God says we become what we think (Pr. 23:7). My belief that the Bible teaches that reincarnation is a fact hasn't endeared me to those who not only reject such an idea but also sincerely believe such a belief comes from the pit of hell and smells of smoke. After reading "Reincarnation in the Bible?" perhaps you can show me where I am in error, if you disagree with me. Or who knows, perhaps you will agree with me. At any rate I hope you find my book interesting and enjoyable, if not enlightening.