The chapter from Volume 1 of "Research-Based Reform of University Physics" presents the background, design, and impact of Peer Instruction. Peer Instruction is an instructional strategy for engaging students during class through a structured questioning process that involves every student. Here we describe Peer Instruction (hereafter PI) and report data from more than ten years of teaching with PI in the calculus- and algebra-based introductory physics courses for non-majors at Harvard University, where this method was developed. Our results indicate increased student mastery of both conceptual reasoning and quantitative problem solving upon implementing PI. Gains in student understanding are greatest when the PI questioning strategy is accompanied by other strategies that increase student engagement, so that every element of the course serves to involve students actively. We also provide data on gains in student understanding and information about implementation obtained from a survey of almost four hundred instructors using PI at other institutions. We find that most of these instructors have had success using PI, and that their students understand basic mechanics concepts at the level characteristic of courses taught with interactive engagement methods. Finally, we provide a sample set of materials for teaching a class with PI, and provide information on the extensive resources available for teaching with PI.