Roberts presents five perplexing but telling existence puzzles that already are or shall soon become important parts of the population ethics literature: the Asymmetry Puzzle, the Pareto Puzzle, the Addition Puzzle, the Anonymity Puzzle, and the Better Chance Puzzle. Roberts develops solutions to the puzzles that together form a partial theory of population, a collection of principles grounded in intuition but highly sensitive to the formal demands of consistency and cogency.