(AggreSet) Datasets commonly include multi-value (set-typed) attributes that describe set memberships over elements, such as genres per movie or courses taken per student. Set-typed attributes describe rich relations across elements, sets, and the set intersections. Increasing the number of sets results in a combinatorial growth of relations and creates scalability challenges. Exploratory tasks (e.g. selection, comparison) have commonly been designed in separation for set-typed attributes, which reduces interface consistency. To improve on scalability and to support rich, contextual exploration of set-typed data, we present AggreSet. AggreSet creates aggregations for each data dimension: sets, set-degrees, set-pair intersections, and other attributes. It visualizes the element count per aggregate using a matrix plot for set-pair intersections, and histograms for set lists, set-degrees and other attributes. Its non-overlapping visual design is scalable to numerous and large sets. AggreSet supports selection, filtering, and comparison as core exploratory tasks. It allows analysis of set relations including subsets, disjoint sets and set intersection strength, and also features perceptual set ordering for detecting patterns in set matrices. Its interaction is designed for rich and rapid data exploration. We demonstrate results on a wide range of datasets from different domains with varying characteristics, and report on expert reviews and a case study using student enrollment and degree data with assistant deans at a major public university.