What are some good introductory books on number theory, combinatorics and algebra?

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Problem

What are some good introductory books on number theory, combinatorics
and algebra?

[ Editor: problem statement reconstructed; the source is an annotated
  reading list without a question. ]

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NUMBER THEORY AND COMBINATORICS

The Higher Arithmetic -Davenport

Numbers: Rational and Irrational -Niven (NML)
    This book was written for bright high school kids along with other
    books of the New Mathematical Library (published by the Mathematical
    Association of America).  Of course very few high schools actually
    use these fine books.  In California it's *illegal* to use them as
    texts in public high schools!  In fact nearly all good books are
    barred, in all subjects.  (cf Surely You're Joking, Mr. Feynman, by
    Feynman).

Mathematics Of Choice -Niven (NML)
    Subtitled "How to count without counting", an introduction to
    combinatorics.

ALGEBRA

A Concrete Approach To Modern Algebra -Sawyer
    "Modern Algebra" is very different from high school algebra.

The Theory Of Equations -V. A. Uspensky
    This on the other hand, picks up where high school algebra left off.

Groups And Their Graphs -Grossman and Magnus (NML)
    Groups should not be confused with sets.  Groups are a sort of
    algebraic structure.  The "graphs" referred to in the title are not
    the type of graph you're thinking of either!

Adventures in Number Theory, by Richard Friedberg:
    Fun, not especially deep.  Contains some of number theory's greatest
    hits, the history of Fermat's last theorem, etc.  You learn that
    Friedberg thinks seven (yes, 7) is dark and mysterious, and that 9
    is sort of blocky.

[ Editor: the list's compiler is not named in the source. ]