Tacit's right. I'll only try to clarify it. The phrase 'у меня есть (книга)' is commonly used and it can be used in most cases. 'Я имею книгу' is grammatically correct, but it sounds weird. The verb 'иметь' is used in formal conversation. 'Иметь' is close to 'own' or 'possess' in meaning. So, you cannot 'иметь' such ordinary objects as a book. But you can say 'я имею автомобиль' which means 'I own a car'. The sentence differs from 'у меня есть машина' which means 'I have a car". You can also say "я имею состояние' - 'I have a fortune'. 'Я имею' can also be used for abstract notions. For instance, 'я имею право' - 'I have a/the right'. You can say 'у меня есть право', but it doesn't sound that serious. I hope this helps. I hope I didn't confuse you more.

I agree with most of the answers. Some additions. If you mean "possess", you need to form you sentence in following way: first - Who has something? - I - у меня; he - у него; she - у нее; they - у них. Second - in English you use "have" or "has", in Russian - есть. It means "есть" is your "have/has". And third - what he/she/they/you have/has? - noun in nominative case (just take it as is from your dictionary). Now lets try: I have a book: 1 - у меня 2 - есть 3 - книга. In order to fully explain you what Andrey means saing "people will laugh for long time". In slang the verb "имею" could be interpreted as "sexual act". I mean the expression"Он имеет somebody" will be traslated "He has a sexual act(s) with somebody". And if "somebody" is book - it looks funny :) But it is too early for you to know such a detail of Great Russian language! I'm joking :)

У меня есть книга is correct. But If you say "я имею книгу" people will laugh for long time )

Правильно: Я имею книгу. У меня есть книга. (in this sentence you should't use "книгу", but "книга") "У меня есть книга." - used most often. "Я имею книгу." - used more rare than the "У меня есть книга." Good luck. (Удачи!)

can not agree with the last one Из песни слов не выкинешь