you will learn some c syntax and things like that, but most of what c++ did was add classes since they dont exist in c, the standard library functions (many handy things not available in c), along with templates, iterators and all kinds of things. c itself is very basic and doesnt have a whole lot that comes with it. i have found its better to learn c first, that way you learn the basic skeleton, and then if you learn c++ you learn all the additions, rather than learn the additions to the language first, and then when you are doing c, have to figure out the hard way what you no longer have anymore.
its also important with c to learn every detail about pointers, character arrays and the memory allocation and string manipulation functions, because c++ gives you the luxury of the string class, which you dont have in c. and going from string to char arrays can be tricky.
the book i recommend to learn c is by the creator himself, its called The C Programming Language. Its the 1989 version so it covers ANSI C89. You can find it in most bookstores that have decent computer sections too.