Despite the numbering of the course as 258B, this course is completely independent of 258A "Numerical Optimization". 

• Bertsimas, Weismantel: Optimization over the Integers, 600 pages, Hardcover, ca. $90. No e-text available, unfortunately
• Laurence A. Wolsey, George L. Nemhauser, Integer and Combinatorial Optimization, 763 pages, Paperback, ca. $110. A comprehensive, older (1988) text.
• Laurence A. Wolsey, Integer Programming, 264 pages, ca. $90-$130. A gentle, and short, introduction to Integer Optimization aimed at the advanced undergraduate and master's level.

Additional reading on combinatorial optimization

Combinatorial optimization is a subfield of discrete optimization, but not the main emphasis in our class.

• William J. Cook, William H. Cunningham, William R. Pulleyblank, Alexander Schrijver, Combinatorial Optimization
• Christos H. Papadimitriou, Kenneth Steiglitz, Combinatorial Optimization: Algorithms and Complexity. A true classic. You can get a paperback of this one for ca. $14
• Bernhard Korte, Jens Vygen, Combinatorial optimization theory and algorithms, Springer, 2008. Available through the UC Library as an e-text free of charge. (If you connect from off-campus, use the UC Library VPN.) You can also order a copy via SpringerLink for $25.

Additional reading on integer optimization

• Alexander Schrijver, Theory of Linear and Integer Programming, ca. $100. An important reference for every researcher in Integer Optimization
• Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, Laurence A. Wolsey (Editors): 50 Years of Integer Programming 1958-2008: From the Early Years to the State-of-the-Art, Hardcover, 804 pages. Among other things, this contains surveys on the most important current research directions in Integer and Nonlinear Mixed-Integer Optimization.
• Jesús A. De Loera, Matthias Köppe, Raymond Hemmecke: Algebraic and Geometric Ideas in the Theory of Discrete Optimization, SIAM, 2012. Why yes, that's my book

Additional reading on Mixed-Integer Nonlinear Optimization and Global Optimization

• Duan Li, Xiaoling Sun, Nonlinear integer programming, Springer, 2006. Available through the UC Library as an e-text free of charge. (If you connect from off-campus, use the UC Library VPN.) You can also order a copy via SpringerLink for $25.
• Ivo Nowak, Relaxation and decomposition methods for mixed integer nonlinear programming, Birkhäuser, 2006. Available through the UC Library as an e-text free of charge. (If you connect from off-campus, use the UC Library VPN.) You can also order a copy via SpringerLink for $25.
• Mohit Tawarmalani, Nikolaos V. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications
• Christodoulos A. Floudas, Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications

Additional reading for a background on linear optimization

Most textbooks on linear optimization give sufficient background.

• Introduction to Linear Optimization by Dimitris Bertsimas and John N. Tsitsiklis
• Linear Programming: Foundations and Extensions by Robert Vanderbei. This is the book that I use in my undergraduate class on Optimization.
• Jon Lee, "A First Course in Linear Optimization", available from https://sites.google.com/site/jonleewebpage/home/publications/

Further resources

• Bradley, Hax, Magnanti: Applied Mathematical Programming. A general introduction to mathematical optimization, including integer linear optimization, from an applied point of view. This is a bit dated (1977), but still a good reading on the basic material from an "operations research" angle. A re-typeset version of this 1977 MIT classic is available online as a full text