Both sentences have a similar meaning, but with some small linguistic difference. "Sobre", is a preposition and when it's used in the sense of your sentence, means that "the book has a support point on the table", it's resting on the table. But remember that you must say "Hay un libro sobre la mesa" or "Hay un libro que está sobre la mesa". "Encima", is an adverb wich indicates in this sentence 'a place more or less immediately superior', but not necessarily in direct contact with the table. The book could be placed on something else that is also on the table. "El libro está encima de la mesa, sobre mis papeles". Anyway, in Spanish is perfectly understandable in either of both cases, and are used interchangeably in everyday language.

Well, this actually is extremly interesting XD. But foremost, the correct expresions you are trying to understand i think would be: "Hay un libro encima de la mesa" and "hay un libro sobre la mesa" (without "esta") Both words can actually be used. In this case either one can have the same meaning. However in different situations you would use one of them specifically. For example: The word "sobre" can refer to something that is right on the thing you are trying to describe, in this case the book is resting right on the table, so you can use "sobre" or "encima" without problem. However imagine for a moment that the the book would be flying or hanging just above the table, without resting on the table itself, in that case you would use "encima" Actually, "sobre" would be the word "on" in english, and the word "encima" would be more aproppriate to translate as "above". But be aware that in many cases like this one, you could use them interchangeably without problems. But if you don't want any misunderstandings when refering to some objects then you should choose carefully For example i would never say that the sun is on my head (sobre mi cabeza) i would say that it's ABOVE my head (encima de mi cabeza)

the correct way to say this phrase is "hay un libro sobre la mesa".. the other phrase is meaningless, as to say "there is a book are the table"... la forma correcta para decir esta frase es "hay un libro sobre la mesa".. la otra frase no tiene sentido alguno, ON solo puede referirse, hablando de lugar, a encima o sobre.

La única diferencia que noto es que ENCIMA se usa con DE y SOBRE se usa sólo. ejemplo: El libro está encima DE la mesa. Las nubes están encima de mi casa. La araña está encima de mi cama. El libro está sobre la mesa. Las nubes están sobre mi casa. La araña está sobre mi cama. there is a book on the table = hay un libro sobre la mesa; hay un libro encima de la mesa. la que yo más uso y más escucho es ENCIMA DE, pero SOBRE también las personas lo usan, yo prefiero usar ENCIMA DE.