Here are some personal (so uneducated) opinions about books.

Hungarians: sorry about the umlauts.

((X) - not in KTHB catalogue)

I'll try to move better books higher up in the list below. They are all good,
however.

I've rated the books with respect to readability only.

 Exceptional
"A course in artihmetic" by Serre
"Mathematical Methods in Mechanics" by Arnold
"Representation theory" by Fulton and Harris
"Introduction to Lie Algebras and Representation Theory" by Humphreys
"Combinatorial Geometry" by Agarwal, Pach
"Graph Theory" by Diestel
"Winning ways for your mathematical plays" by 

 The rest
"Linear representations of finite groups" by Jean-Paul Serre
"A course in combinatorics" by van Lint and Wilson
"Coffee time in Memphis" by Bollobas
"Algebraic combinatorics on words" by Lothaire
"Discrete Geometry" by Jiri Matousek
"The symmetric group" by Bruce Sagan
"Ordinary Differential Equations" by Vladimir Arnold
"Combinatorial Problems and Exercises" by Laszlo Lovasz
"Mathematical Puzzles" by Peter Winkler
"Problems in Mathematical Analysis" (I and II) by Polya and Szego
"Enumerative combinatorics" by Stanley
Also, http://www.math.mit.edu/~rstan/bij.pdf
"Tilings and patterns" by Grünbaum and Shephard
"The art and craft of problem solving" by Zeitz
"Problems for mathematicians young and old" by Halmos
"Mathematical Puzzles: A connaisseur's collection" by Winkler
"Geometric folding algorithms" by Demaine and Demaine (X)
"Additive combinatorics" by Tao and Vu
"Introduction to Geometry" by Coxeter
"The Geometry of Physics" by Theodore Frankel
"Algebraic Topology" by Allen Hatcher
"On Numbers And Games" by John Conway
"Analytics Combinatorics" by 
"A course in enumeration" by Martin Aigner
"The probabilistic method" by Noga Alon and Joel Spencer
"Algebra" by Lang
"Theory group theory of finite order" by W. Burnside
"An introduction to the theory of numbers" by Hardy and Wright (and Silverman
and Wiles)
"Extremal Graph Theory" by Bela Bollobas
"Combinatorial Matrix Classes" by Brualdi
(something similar) by Brualdi and Ryser

   Stuff
"Intuitive topology" by Prasolov
"The Mathematical Experience" by Davis
"Calculus" by Spivak
"Mathematical Analysis" by Walter Rudin
"The mathematical mechanic: using physical reasoning to solve problems" by Mark
Levi
"Projective geometries over finite fields" by Hirschfeld. Fun: includes
specific descriptions of the smallest projective planes (up to order 13
(10'sn't mentioned)).
"Substitutions in Dynamics, Arithmetics and Combinatorics" by Pytheas Fogg
"Topology from the differentiable viewpoint" by Milnor
"Thirty-three miniatures: Mathematical and Algorithmic Applications of Linear
Algebra" by Jiri Matousek (X)
"The Emergence of the Theory of Lie Groups: An Essay in the History of. Mathematics, 1869–1926" by Thomas Hawkins
"J. K. Edmonds. A combinatorial representation for polyhedral surfaces, Notices
Amer.Math. Soc. (1960), 646."
"Computers and intractability: A guide to NP-completeness"
Harary, F. (1974), "A survey of the reconstruction conjecture", Graphs and Combinatorics. Lecture Notes in Mathematics 406, Springer, pp. 18–28,doi:10.1007/BFb0066431
Ronald C. Read1, Derek G. Corneil: "The graph isomorphism disease"
"Computable functions" by Nikolai Konstantinovich Vereshchagin, Alexander Shen
"A lifetime of puzzles" by Demaine
"Combinatorics, Automata and Number Theory" röd bok
Khinchin: "Continued fractions"
"Elements of the Representation Theory of Associative Algebras" by Assem,
Simson, Skowrónski
"Combinatorics and Commutative Algebra" by Stanley
"Algorithmic Game Theory" by Nisan et. al.
"Dynamics, Statistics and Projective Geometry of Galois Fields" by Arnold
"Simple games" by Taylor and Zwicker

 Other heading

"Rotation distance, triangulations and hyperbolic geometry" by Sleator,
Tarjan, Thurston

 Diversions
"An Application of Poincare's Recurrence Theorem to Academic Administration"
http://www.cs.umd.edu/~gasarch/papers/poll.pdf