"The Department of Mathematics at the University of Illinois at Urbana-Champaign has long been known for the strength of its program in number theory. The department has a large and distinguished faculty noted for their work in this area, and the graduate program in number theory attracts students from throughout the world. At present over twenty students are writing dissertations in number theory. Each semester upper level graduate courses are offered in a variety of topics in analytic, algebraic, combinatorial, and elementary number theory." from Number Theory, Department of Mathematics, University of Illinois at Urbana-Champaign
Books on number theory can be found in the Mathemathics Library Stacks on the main level shelved under call number range 512.7 to 512.788.
"number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of mathematical pursuits." from "number theory." Encyclopaedia Britannica. Encyclopaedia Britannica Online Academic Edition. Encyclopædia Britannica Inc., 2015. Web. 12 Feb. 2015.
"The basic concepts of number theory include the classification of numbers into different sets of special importance, the notion of divisibility, and the representation of integers." from Grantham, Jon, et al. "Number Theory." Handbook of Discrete and Combinatorial Mathematics. Ed. Kenneth H. Rosen, et al. Boca Raton, Fla. : CRC Press, 2000. PDF e-book.
"Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and prime factorization are especially important in number theory, as are a number of functions such as the divisor function, Riemann zeta function, and totient function." from Number Theory -- from Wolfram MathWorld.