"The graduate program in mathematical logic at the University of Illinois at Urbana-Champaign is one of the most active such programs in the world, with a large community of faculty and students. Most aspects of the subject are represented here, especially model theory and its applications and descriptive set theory. A particular emphasis of our program is on the connections of logic to other important areas of mathematics." from Logic, Department of Mathematics, University of Illinois at Urbana-Champaign
Books on logic can be found in the Mathemathics Library Stacks on the main level shelved under call number 511.3 to 511.4.
"Logic is "the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof." from Logic -- from Wolfram MathWorld.
"A very simple form of logic is the study of 'truth tables' and digital logic circuits in which one or more outputs depend on a combination of circuit elements (AND, OR, NAND, NOR, NOT, XOR, etc.; 'gates') and the input values. In such a circuit, values at each point can take on values of only TRUE(1) or FALSE(0)." from Eric W. Weisstein "Logic". CRC Concise Encyclopedia of Mathematics. 2nd Ed. Boca Raton, Fla. : CRC Press, 2003. PDF e-book.
"Logic is the basis of all reasoned argument; and, therefore, logic is the basis for valid mathematical proofs." from Charles E . Roberts "Logic". Introduction to Mathematical Proofs Ed. Denny Gulick Boca Raton, Fla. : CRC Press, 2009. PDF e-book.