Double Dual Vector Space

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Consider only finite-dimensional spaces; I know that infinite-dimensional spaces are different. Let V be a finite-dimensional vector space, V* its dual, and V** its double-dual. I do not understand how V** is "naturally isomorphic" to V? As nearly as I can tell, V** is no better than V*. The answers on this forum are too confusing. Is there anyone kind enough to give me a very detailed answer? I need all the nuts and bolts. I haven't seen an answer on the internet that I have liked.