reference request for construction of expanders
You can look at this survey by Hoory, Linial, and Wigderson [1]. Chapter 9, specifically (p. 508) is on the zigzag product.

9.The zig-zag product
  9.1.   Introduction
  9.2.   Construction of an expander family using zig-zag
  9.3.   Definition and analysis of the zig-zag product
  9.4.   Entropy analysis
  9.5.   An application to complexity theory: SL=L



[1] Hoory, Shlomo, Nathan Linial, and Avi Wigderson. Expander graphs and their applications. Bulletin of the American Mathematical Society 43.4 (2006): 439-561.