Introduction to Algorithms by Thomas H. Cormen, Charles E. Leiserson and Ronald L. Rivest and Clifford Stein : Chapter 27

The authors define the concept of a comparator and a wire. The authors extend it to input wires and output wires and input sequence and output sequence. The authors also define the concept of comparison network and lines. The authors define the concept of depth of a wire as well as the time it takes for a comparison network to generate output. The author also defined the concept of sorting network.

The authors describe and prove Zero-one principal for sorting networks which says that if a sorting network works correctly when each input is drawn from set $\{0,1\}$, then it works correctly on arbitrary input numbers.

The authors then provide the concept of bitonic sequence, a sequence that monotonically increases and then monotonically decreases. A bitonic sorter is a comparison network that sorts bitonic sequence. Every stage of a bitonic sorter is called half-cleaner. The authors then prove some lemmas and describe how to build bitonic sorter from half-cleaner.

The authors then provide the design of a merge network.