I suggest you to read the book "C++ How to Program" By Paul Deitel , Harvey Deitel. I think this book provides a complete basis of fundamental instruction in all core aspects of C++.
One of the best beginners book is C++ Primer (5th Edition) by S. B. Lippman, J. Lajoie, B. E. Moo
My second choice for a C++ beginner book is C++ Primer Plus by Stephen Prata, this book also presents the new C++11 syntax
Written by the author of the C++ language Bjarne Stroustroup Programming: Principles and Practice Using C++ is also a good choice for a beginner
Another good book for a C++ beginner that has some programming experience with other programming language is Accelerated C++: Practical Programming by Example by Andrew Koenig:
My last choice for this list is Professional C++ by M. Gregoire, N. A. Solter, S. J. Kleper 2nd edition. This book can be used in pair with one of the above, if you want to learn the new C++11 syntax. Not recommended for a complete beginner.
Thank you very much for your comments and advices! They are really helpful!
Dr. Osama Y. Al-Rawi, the problem is that there are too many books on C++. Some of them are very informative and, I would say, educational, and some of them are not so good. That is why I ask the advice of an expert.