I have to say nothing more than the others; perhaps only clarifying a few things:
Stroustrup's book is a very good suggestion, as he's the father of C++ language, so that he introduces not only the language, but he also does it in the way a C++ programmer should think.
The Eckel's book goes exactly in the same direction (you can see it also from the title), and that's the most important thing in a programming language or in any other laguage, also human: thinking natively in that language.
The file string.h is an (now they say) old C library needed to perform library operations on memory and strings (typically, string and memory concatenation, copy, movement, setting, comparison, searching, etc.).
It should come with any C/C++ development package, as it is ANSI C, and you can easily have a look at it with any editor as it is an ASCII file, BUT don't edit it! You will find mainly function declarations and the definition of the size_t type.
Hope it helped!
Marino