Books:
[WS]The Design of Approximation Algorithms by David Williamson and David Shmoys, Cambridge University Press, 2011. https://www.designofapproxalgs.com/book.pdf
[VV]Approximation Algorithms by Vijay Vazirani, Springer-Verlag, 2004. https://www.ics.uci.edu/~vazirani/book.pdf
My lecture notes
Greedy Paradigm
CHRISTOFIDES 3/2-FACTOR for TSP
INAPPROXIMABILITY for GENERAL TSP
APPROXIMATION PRESERVING REDUCTION FOR GENERAL STEINER TREE
GREEDY-K CENTER PROBLEM and INAPPROXIMABILITY OF K CENTER
Local Search Paradigm
LOCAL SEARCH-MINIMIZING MAKESPAN
Scaling and Rounding
Random Sampling
Linear Programming Paradigm
RANDOMIZED ROUNDING MIN SET COVER
RANDOMIZED ROUNDING MAX INDEPENDENT SET
PRIMAL DUAL - VERTEX COVER and SET COVER
PRIMAL DUAl - PRIZE COLLECTING VERTEX COVER