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As the title suggests, I am looking for recommendations on introductory books to Sieve Theory. Please include a brief explanation of your experience with the book in your answer.
"An Introduction to Sieve Methods and Their Applications" by Murty and Cojocaru, and "Sieves in Number Theory" by Greaves are good introductions to the subject. "Opera De Cribro" by Friedlander and Iwaniec is the most comprehensive and up to date text. "Sieve Methods" by Halberstam and Richert is the classic text. It is a bit dated but offers a good historical perspective.