Question: > 
> To that great man, I dedicate this book to.
> 
> 
> 

Is this correct? I'm wondering if it's alright to end a sentence with a to proposition at the end.

Answer: 
You can have either of the *to*'s, but not both; but the meaning is different. 

> 
> To that great man, I dedicate this book.
> 
> 
> 

is a perfectly good sentence. It's a non-standard word order (more normal would be "I dedicate this book to that great man") so it has the effect of emphasising the great man. 

> 
> That great man I dedicate this book to.
> 
> 
> 

(preferably without the comma) is a sentence fragment: there is an implied relative pronoun "That great man that/who/whom I dedicate this book to", so the fragment is a complex noun phrase, not a whole sentence. To make it a whole sentence you need a main verb:

> 
> That great man I dedicate this book to is John Smith.
> 
> 
> 

But in a suitable conversational context, a sentence fragment like that can stand on its own.
In this case the second *to* is wrong because the sentence already has one (at the beginning).

In the past, prepositions at the end of the sentence are termed "stranded prepositions" and regarded as a stylistic flaw, if not even grammatically wrong. More modern linguists and style guides, however, regard them as something that's perfectly permissible.

[Source:](http://blog.oxforddictionaries.com/2011/11/grammar-myths-prepositions/) 

Personally, prepositions at the end of a sentence are nothing I object **to**. Ba-dum-tsss!